The effect of supplementary feeds on the bodyweight of yaks in cold season

The present study was conducted to determine the effects of supplementary feeds, oat hay (OH), highland barley straw (HBS) and multi-nutrient blocks supplementation (UMMB) on reducing liveweight losses of both yak cows and calves grazed on low quality pastures during cold season. The trials of OH and HBS supplementation were conducted by using completely random design on 104 yak cows between 6 and 12 years of age as the following treatments: pure grazing (41 animals, body weight 230 67 kg) as control (CK); grazing+1.5 kg DM of OH per head daily (30 animals, body weight 216 28 kg); gazing. 1.5 kg DM of HBS per head daily (33 animals, body weight 221 34 kg). The trial of UMMB was conducted on three types of yaks, 1-year calves (8-12 months old, body weight 61.1 6.9 kg), 2-year calves (18-24 months old, 98.0 11.3 kg) and yak cows (164.5 27.1 (S.D.) kg) with 20 animals in control group (CK) and 20 animals in supplement group for each type by using completely random design as the following treatments: pure grazing for CK group; grazing+ 150, 250 and 500 g UMMB per day averagely for 1-year calf, 2-year calf and cow at night. The results indicate that the animals supplemented with oat hay received body weight gain (32 20.7 g day(-1)), while those supplemented with highland barley straw still suffered from body weight loss (-56.7 39.3 a day(-1)); UMMB supplementation can decrease the body weight loss by 109.7%, 86.6% and 63.4% for the 1-year calves, 2-year calves and yak cows, respectively, as compared with pure grazing. Around US$1.60 output can be achieved on the basis of US$1 input for UMMB supplementation in the farming systems of the 1-year calves, 2-year calves and yak cows, while US$1 input can produce US$1.55 and 1.14 output for OH and FIBS supplementations, respectively, in yak cows' farming system. It can be preliminary concluded that UMMB supplementation was the most economic way to alleviate body weight loss of grazing yaks over cold season, and the higher productive returns were obtained from OH supplementation for grazing yak cows during winter/spring months. © 2004 Elsevier B.V All rights reserved.

Urbanization effects on welfare and income diversification strategies of peri-urban farm households in Tigray, Northern Ethiopia: An empirical analysis

Urban areas in many developing countries are expanding rapidly by incorporating nearby subsistence farming communities. This has a direct effect on the consumption and production behaviours of the farm households but empirical evidence is sparse. This thesis investigated the effects of rapid urbanization and the associated policies on welfare of subsistence farm households in peri-urban areas using a panel dataset from Tigray, Ethiopia. The study revealed a number of important issues emerging with the rapid urban expansion. Firstly, private asset holdings and consumption expenditure of farm households, that have been incorporated into urban administration, has decreased. Secondly, factors that influence the farm households’ welfare and vulnerability depend on the administration they belong to, urban or rural. Gender and literacy of the household head have significant roles for the urban farm households to fall back into and/or move out of poverty. However, livestock holding and share of farm income are the most important factors for rural households. Thirdly, the study discloses that farming continues to be important source of income and income diversification is the principal strategy. Participation in nonfarm employment is less for farm households in urban than rural areas. Adult labour, size of the local market and past experience in the nonfarm sector improves the likelihood of engaging in skilled nonfarm employment opportunities. But money, given as compensation for the land taken away, is not crucial for the household to engage in better paying nonfarm employments. Production behaviour of the better-off farm households is the same, regardless of the administration they belong to. However, the urban poor participate less in nonfarm employment compared to the rural poor. These findings signify the gradual development of urban-induced poverty in peri-urban areas. In the case of labour poor households, introducing urban safety net programmes could improve asset productivity and provide further protection.

Optimising sorting and washing of home-grown maize to reduce fumonisin contamination under laboratory-controlled conditions

Subsistence farming communities with low socio-economic status reliant on a mono cereal maize diet are exposed to fumonisin levels that exceed the provisional maximum tolerable daily intake of 2 mu g kg(-1) body weight day(-1) recommended by the Joint FAO/WHO Expert Committee on Food Additives. In the rural Centane magisterial district, Eastern Cape Province, South Africa, it is customary during food preparation to sort visibly infected maize kernels from good maize kernels and to wash the good kernels prior to cooking. However, this customary practice seems not to sufficiently reduce the fumonisin levels. This is the first study to optimise the reduction of fumonisin mycotoxins in home-grown maize based on customary methods of a rural population, under laboratory-controlled conditions. Maize obtained from subsistence farmers was analysed for the major naturally occurring fumonisins (FB1, FB2 and FB3) by fluorescence HPLC. Large variations were observed in the unsorted and the experimental maize batches attributable to the non-homogeneous distribution of fumonisin contamination in maize kernels. Optimised hand-sorting of maize kernels by removing the visibly infected/damaged kernels (fumonisins, 53.7 +/- 15.0 mg kg(-1), 2.5% by weight) reduced the mean fumonisins from 2.32 +/- 1.16 mg kg(-1) to 0.68 +/- 0.42 mg kg(-1). Hand washing of the sorted good maize kernels for a period of 10 min at 25 degrees C resulted in optimal reduction with no additional improvement for wash periods up to 15 h. The laboratory optimised sorting reduced the fumonisins by 71 +/- 18% and an additional 13 +/- 12% with the 10 min wash. Based on these results and on local practices and practicalities the protocol that would be recommended to subsistence farmers consists of the removal of the infected/damaged kernels from the maize followed by a 10 min ambient temperature water wash. (C) 2010 Elsevier Ltd. All rights reserved.

Mycotoxins and human disease: a largely ignored global health issue

Aflatoxins and fumonisins (FB) are mycotoxins contaminating a large fraction of the world's food, including maize, cereals, groundnuts and tree nuts. The toxins frequently co-occur in maize. Where these commodities are dietary staples, for example, in parts of Africa, Asia and Latin America, the contamination translates to high-level chronic exposure. This is particularly true in subsistence farming communities where regulations to control exposure are either non-existent or practically unenforceable. Aflatoxins are hepatocarcinogenic in humans, particularly in conjunction with chronic hepatitis B virus infection, and cause aflatoxicosis in episodic poisoning outbreaks. In animals, these toxins also impair growth and are immunosuppressive; the latter effects are of increasing interest in human populations. FB have been reported to induce liver and kidney tumours in rodents and are classified as Group 2B 'possibly carcinogenic to humans', with ecological studies implying a possible link to increased oesophageal cancer. Recent studies also suggest that the FB may cause neural tube defects in some maize-consuming populations. There is a plausible mechanism for this effect via a disruption of ceramide synthase and sphingolipid biosynthesis. Notwithstanding the need for a better evidence-base on mycotoxins and human health, supported by better biomarkers of exposure and effect in epidemiological studies, the existing data are sufficient to prioritize exposure reduction in vulnerable populations. For both toxins, there are a number of practical primary and secondary prevention strategies which could be beneficial if the political will and financial investment can be applied to what remains a largely and rather shamefully ignored global health issue.

Agriculture, settlement and society in Early Medieval Ireland

During the early medieval period, Ireland was politically organised into a large number of very small kingdoms. Unlike much of Western Europe, it had not been incorporated into the Roman Empire, and as a consequence, settlement remained exclusively rural in character until the Viking period. Extensive documentary, archaeological, zooarchaeological and macro-plant evidence provides a detailed reconstruction of the livestock and arable economy of the period. Cattle ownership formed the basis of wealth as well as being an indicator of status in society, and this is reflected in its clear dominance of the livestock economy during this period. From the eighth century onwards, however, cereal production appears to grow in importance as subsistence farming gave way to the production of agricultural surplus. This is reflected in cereal diversification and in the construction of watermills and more efficient grain-drying kilns. At the same time, settlement underwent significant changes and the relative importance of cattle in some areas began to decline.

Aflatoxin Exposure and Associated Human Health Effects, a Review of Epidemiological Studies

flatoxins are fungal toxins that possess acute life threatening toxicity, carcinogenic properties and other potential chronic adverse effects. Dietary exposure to aflatoxins is considered a major public health concern, especially for subsistence farming communities in sub-Saharan Africa and South Asia, where dietary staple food crops such as groundnuts and maize are often highly contaminated with aflatoxin due to hot and humid climates and poor storage, together with low awareness of risk and lack of enforcement of regulatory limits. Biomarkers have been developed and applied in many epidemiological studies assessing aflatoxin exposure and the associated health effects in these high-risk population groups. This review discusses the recent epidemiological evidence for aflatoxin exposure, co-exposure with other mycotoxins and associated health effects in order to provide evidence on risk assessment, and highlight areas where further research is necessary. Aflatoxin exposure can occur at any stage of life and is a major risk factor for hepatocellular carcinoma, especially when hepatitis B infection is present. Recent evidence suggests that aflatoxin may be an underlying determinant of stunted child growth, and may lower cell-mediated immunity, thereby increasing disease susceptibility. However, a causal relationship between aflatoxin exposure and these latter adverse health outcomes has not been established, and the biological mechanisms for these have not been elucidated, prompting further research. Furthermore, there is a dearth of information regarding the health effects of co-exposure to aflatoxin with other mycotoxins. Recent developments of biomarkers provide opportunities for important future research in this area.

L'adaptation des agriculteurs vivriers du Sénégal au changement climatique : cas de la communauté rurale de Sessène

Le Sénégal est situé dans une zone soudano-sahélienne particulièrement exposée aux changements du climat, ce dernier rendant l’agriculture, activité principale du pays, précaire. La modification des conditions climatiques, en particulier depuis la fin des années 1960, a fortement affaibli le secteur agricole, majoritairement vivrier et pluvial. Face à l’importance de l’activité agraire vivrière du pays, il apparaît primordial de savoir comment les agriculteurs vivriers du Sénégal ont modifié ou prévoit modifier leurs pratiques en vue de satisfaire leurs besoins alimentaires dans un contexte de changement et de variabilité du climat. Cette étude a été effectuée au sein de la communauté rurale de Sessène selon une approche qualitative et à l’aide d’entretiens, de l’observation participante et d’analyse phénoménologique. Elle a permis de mettre en avant les caractéristiques générales des familles agraires et des exploitations de cette zone, de montrer comment les agriculteurs ont vécu le changement climatique et comment ils envisagent les prochaines années et enfin de discuter de leur capacité d’adaptation. Face au raccourcissement de la saison des pluies, à la diminution des précipitations, à l’intensification des évènements extrêmes et aux impacts de ces modifications sur l’environnement naturel, les agriculteurs vivriers adoptent des mesures aussi bien techniques que socio-économiques.

The role of ligneous vegetation for livestock nutrition in the sub-Sahelian and Sudanian zones of West Africa: Potential effects of climate change

Climate change and variability in sub-Saharan West Africa is expected to have negative consequences for crop and livestock farming due to the strong dependence of these sectors on rainfall and natural resources, and the low adaptive capacity of crops farmers, agro-pastoralist and pastoralists in the region. The objective of this PhD research was to investigate the anticipated impacts of expected future climate change and variability on nutrition and grazing management of livestock in the prevailing extensive agro-pastoral and pastoral systems of the Sahelian and Sudanian zones of Burkina Faso. To achieve this, three studies were undertaken in selected village territories (100 km² each) in the southern Sahelian (Taffogo), northern Sudanian (Nobere, Safane) and southern Sudanian (Sokouraba) zone of the country during 2009 and 2010. The choice of two villages in the northern Sudanian zone was guided by the dichotomy between intense agricultural land use and high population density near Safane, and lower agricultural land use in the tampon zone between the village of Nobere and the National Park Kaboré Tambi of Pô. Using global positioning and geographical information systems tools, the spatio-temporal variation in the use of grazing areas by cattle, sheep and goats, and in their foraging behaviour in the four villages was assessed by monitoring three herds each per species during a one-year cycle (Chapter 2). Maximum itinerary lengths (km/d) were observed in the hot dry season (March-May); they were longer for sheep (18.8) and cattle (17.4) than for goats (10.5, p<0.05). Daily total grazing time spent on pasture ranged from 6 - 11 h with cattle staying longer on pasture than small ruminants (p<0.05). Feeding time accounted for 52% - 72% of daily time on pasture, irrespective of species. Herds spent longer time on pasture and walked farther distances in the southern Sahelian than the two Sudanian zones (p<0.01), while daily feeding time was longer in the southern Sudanian than in the other two zones (p>0.05). Proportional time spent resting decreased from the rainy (June - October) to the cool (November - February) and hot dry season (p<0.05), while in parallel the proportion of walking time increased. Feeding time of all species was to a significantly high proportion spent on wooded land (tree crown cover 5-10%, or shrub cover >10%) in the southern Sahelian zone, and on forest land (tree crown cover >10%) in the two Sudanian zones, irrespective of season. It is concluded that with the expansion of cropland in the whole region, remaining islands of wooded land, including also fields fallowed for three or more years with their considerable shrub cover, are particularly valuable pasturing areas for ruminant stock. Measures must be taken that counteract the shrinking of wooded land and forests across the whole region, including also active protection and (re)establishment of drought-tolerant fodder trees. Observation of the selection behaviour of the above herds of cattle and small ruminant as far as browse species were concerned, and interviews with 75 of Fulani livestock keepers on use of browse as feed by their ruminant stock and as remedies for animal disease treatment was undertaken (Chapter 3) in order to evaluate the consequence of climate change for the contribution of browse to livestock nutrition and animal health in the extensive grazing-based livestock systems. The results indicated that grazing cattle and small ruminants do make considerable use of browse species on pasture across the studied agro-ecological zones. Goats spent more time (p<0.01) feeding on browse species than sheep and cattle, which spent a low to moderate proportion of their feeding time on browsing in any of the study sites. As far as the agro-ecological zones were concerned, the contribution of browse species to livestock nutrition was more important in the southern Sahelian and northern Sudanian zone than the southern Sudanian zone, and this contribution is higher during the cold and hot dry season than during the rainy season. A total of 75 browse species were selected on pasture year around, whereby cattle strongly preferred Afzelia africana, Pterocarpus erinaceus and Piliostigma sp., while sheep and goats primarily fed on Balanites aegyptiaca, Ziziphus mauritiana and Acacia sp. Crude protein concentration (in DM) of pods or fruits of the most important browse species selected by goats, sheep and cattle ranged from 7% to 13% for pods, and from 10% to 18% for foliage. The concentration of digestible organic matter of preferred browse species mostly ranged from 40% to 60%, and the concentrations of total phenols, condensed tannins and acid detergent lignin were low. Linear regression analyses showed that browse preference on pasture is strongly related to its contents (% of DM) of CP, ADF, NDF and OM digestibility. Interviewed livestock keepers reported that browse species are increasingly use by their grazing animals, while for animal health care use of tree- and shrub-based remedies decreased over the last two decades. It is concluded that due to climate change with expected negative impact on the productivity of the herbaceous layer of communal pastures browse fodder will gain in importance for animal nutrition. Therefore re-establishment and dissemination of locally adapted browse species preferred by ruminants is needed to increase the nutritional situation of ruminant stock in the region and contribute to species diversity and soil fertility restoration in degraded pasture areas. In Chapter 4 a combination of household surveys and participatory research approaches was used in the four villages, and additionally in the village of Zogoré (southern Sahelian zone) and of Karangasso Vigué (northern Sudanian zone) to investigate pastoralists’ (n= 76) and agro-pastoralists’ (n= 83) perception of climate change, and their adaptation strategies in crop and livestock production at farm level. Across the three agro-ecological zones, the majority of the interviewees perceived an increase in maximum day temperatures and decrease of total annual rainfall over the last two decades. Perceptions of change in climate patterns were in line with meteorological data for increased temperatures while for total rainfall farmers’ views contrasted the rainfall records which showed a slight increase of precipitation. According to all interviewees climate change and variability have negative impacts on their crop and animal husbandry, and most of them already adopted some coping and adaptation strategies at farm level to secure their livelihoods and reduce negative impacts on their farming system. Although these strategies are valuable and can help crop and livestock farmers to cope with the recurrent droughts and climate variability, they are not effective against expected extreme climate events. Governmental and non-governmental organisations should develop effective policies and strategies at local, regional and national level to support farmers in their endeavours to cope with climate change phenomena; measures should be site-specific and take into account farmers’ experiences and strategies already in place.

Identifying the factors governing attitude towards the e-Agriservice among dairy farmers in Maharashtra, India

Information and communication technology (ICT) projects have a great potential to revolutionise the information delivery system by bridging the gap between farmers and extension personnel. aAQUA (Almost All Questions Answered) portal was launched by the Developmental Informatics Laboratory (DIL) at Indian Institute of Technology (IIT) Mumbai, Maharashtra, India in 2003 as an information providing system to deliver technology options and tailored information for the problems and queries raised by Indian dairy farmers. To measure the effectiveness of this service the attitudinal dimensions of the users of aAQUA e-Agriservice were investigated using a 22 item scale. A simple random sampling technique was used to select 120 dairy farmers from which data were collected and subjected to factor analysis to identify the underlying constructs in this research. From the attitude items, four components were extracted and named as the pessimistic, utility, technical and efficacy perspective, which influenced the development of varied level of attitudinal inclination towards the e-Agriservice. These components explained 64.40 per cent of variation in the attitude of the users towards the aAQUA e-Agriservice. This study provides a framework for technically efficient service provision that might help to reduce the pessimistic attitude of target population to adopt e-Agriservice in their farming system. The results should also be helpful for researchers, academics, ICT based service providers and policy makers to consider these perspectives while planning and implementing ICT projects.

Identifying and understanding factors influencing the uptake of new technologies on dairy farms in SW England using the theory of reasoned action

Whilst much is known of new technology adopters, little research has addressed the role of their attitudes in adoption decisions; particularly, for technologies with evident economic potential that have not been taken up by farmers. This paper presents recent research that has used a new approach which examines the role that adopters' attitudes play in identifying the drivers of and barriers to adoption. The study was concerned with technologies for livestock farming systems in SW England, specifically oestrus detection, nitrogen supply management, and, inclusion of white clover. The adoption behaviour is analysed using the social-psychology theory of reasoned action to identify factors that affect the adoption of technologies, which are confirmed using principal components analysis. The results presented here relate to the specific adoption behaviour regarding the Milk Development Council's recommended observation times for heat detection. The factors that affect the adoption of this technology are: cost effectiveness, improved detection and conception rates as the main drivers, whilst the threat to demean the personal knowledge and skills of a farmer in 'knowing' their cows is a barrier. This research shows clearly that promotion of a technology and transfer of knowledge for a farming system need to take account of the beliefs and attitudes of potential adopters. (C) 2006 Elsevier Ltd. All rights reserved.

A cross-sectional study of reproductive performance of smallholder dairy cows in coastal Tanzania

A retrospective cross-sectional study was conducted on 200 randomly selected smallholder farms from a mixed dairy farming system in Tanga, Tanzania, between January and April 1999. We estimated the frequency and determinants of long calving interval (LCI), retention of fetal membrane (RFM), dystocia, and abortion in smallholder crossbred cattle and explored birth trends. The mean calving interval was 500 days and birth rate was 65 per 100 cow-years. Dystocia was reported to affect 58% of calvings, and 17.2% of animals suffered RFM. Using mixed effect models, the variables associated with LCI, RFM and dystocia were breed, level of exotic blood and condition score. Zebu breeding was associated with LCI (odds ratio (OR) = 2.3, p = 0.041) and Friesian breeding with lower odds for RF (OR = 0.26, p = 0.020). Animals with higher levels of exotic blood had lower odds for evidence of dystocia (OR = 0.45, p = 0.021). Evidence of dystocia was significantly associated with poor condition score (beta = -1.10, p = 0.001). Our observations suggest that LCIs are common in smallholder dairy farms in this region and a likely source of economic loss. Dystocia, RFM, poor condition score and mineral deficiency were common problems and were possibly linked to LCI.

Land use intensity and trees on farms in Malawi

Rapidly increasing population densities in Malawi have put a huge strain on the existing agricultural land and the surrounding woodland. Smallholder agriculture is the dominant economic activity of Malawi’s rural population and many farmers have been forced to cultivate marginal lands with less fertile soils, making conditions much more difficult to grow crops. Natural woodland is under increasing pressure from the opening of new lands for cultivation and the increased demand for firewood, timber and other woody resources, with rural households historically obtaining most of their complementary inputs and saleable commodities from nearby areas of forest (Arnold, 1997a). Despite this increasing pressure, woodlands are not being cleared indiscriminately; selected indigenous species are left standing in fields and around households. These are joined by exotic species that are planted and maintained. These trees provide products and services that are vital, yielding food, firewood, building materials and medicine, replenishing soil fertility and protecting against soil erosion. Following a Boserupian approach, this study attempts to establish the reality of a trajectory of enhanced on-farm tree planting and management as population pressure mounts and as part of a more general process of agricultural intensification. The study examines the combination of factors (social, economic, political and environmental) that either stimulate or discourage on-farm tree planting on smallholdings in Malawi, highlighting how woodland resource use changes over a gradient of land use intensity. This study gives a detailed insight into the way that tree planting and management in the smallholder farming system in Malawi works and identifies a trend of increased tree planting/management alongside an increase in agricultural intensification. However, there is no single ‘path’ of intensification; the link between agricultural change and tree planting is complex and there are many trajectories of intensification that a farmer may follow, dependent on his/her social or economic circumstances. The study recommends that agroforestry interventions give rigorous consideration to the needs of the local community, and the suitability of trees to address those needs, before embarking on programmes that advocate tree planting and management as a panacea.

Natural disaster accounting bias and its equivalence across genetic resource stocks

Two sources of bias arise in conventional loss predictions in the wake of natural disasters. One source of bias stems from neglect of accounting for animal genetic resource loss. A second source of bias stems from failure to identify, in addition to the direct effects of such loss, the indirect effects arising from implications impacting animal-human interactions. We argue that, in some contexts, the magnitude of bias imputed by neglecting animal genetic resource stocks is substantial. We show, in addition, and contrary to popular belief, that the biases attributable to losses in distinct genetic resource stocks are very likely to be the same. We derive the formal equivalence across the distinct resource stocks by deriving an envelope result in a model that forms the mainstay of enquiry in subsistence farming and we validate the theory, empirically, in a World-Society-for-the-Protection-of-Animals application

Diversity for resilience : multi-scale application of agro-ecology

The integration of ecological principles into agricultural systems presents major opportunities for spreading risk at the crop and farm scale. This paper presents mechanisms by which diversity at several scales within the farming system can increase the stability of production. Diversity of above- and below-ground biota, but also genetic and phenotypic diversity within crops, has an essential role in safeguarding farm production. Novel mixtures of legume-grass leys have been shown to potentially provide significant benefits for pollinator and decomposer ecosystem services but to realise the greatest improvements carefully tailored farm management is needed such as mowing or grazing time, and the type and depth of cutivation. Complex farmland landscapes such as agroforestry systems have the potential to support pollinator abundance and diversity and spread risk across production enterprises. At the crop level, early results indicate that the vulnerability of pollen development, flowering and early grain set to abiotic stress can be ameliorated by managing flowering time through genotypic selection, and through the buffering effects of pollinators. Finally, the risk of sub-optimal quality in cereals can be mitigated through integration of near isogenic lines selected to escape specific abiotic stress events. We conclude that genotypic, phenotypic and community diversity can all be increased at multiple scales to enhance resilience in agricultural systems.

Multiple-criteria decision analysis for integrated catchment management

Implementation of integrated catchment management (ICM) is hampered by the lack of a conceptual framework for explaining how landowners select farming systems for their properties. Benefit–cost analysis (a procedure that estimates the costs and benefits of alternative actions or policies) has limitations in this regard, which might be overcome by using multiple-criteria decision analysis (MCDA). MCDA evaluates and ranks alternatives based on a landowner's preferences (weights) for multiple-criteria and the values of those criteria. A MCDA approach to ICM is superior to benefit–cost analysis which focuses only on the monetary benefits and costs, because it: 1) recognizes that human activities within a catchment are motivated by multiple and often competing criteria and/or constraints; 2) does not require monetary valuation of criteria; 3) allows trade-offs between criteria to be measured and evaluated; 4) explicitly considers how the spatial configuration of farming systems in a catchment influences the values of criteria; 5) is comprehensive, knowledge-based, and stakeholder oriented which greatly increases the likelihood of resolving catchment problems; and 6) allows consideration of the fairness and sustainability of land and water resource management decisions. A MCDA based on an additive, multiple-criteria utility function containing five economic and environmental criteria was used to score and rank five farming systems. The rankings were based on the average criteria weights for a sample of 20 farmers in a US catchment. The most profitable farming system was the lowest-ranked farming system. Three possible reasons for this result are evaluated. First, the MCDA method might cause respondents to express socially acceptable attitudes towards environmental criteria even when they are not important from a personal viewpoint. Second, the MCDA method could inflate the ranks of less profitable farming systems for the simple reason that it allows the respondent to assign non-zero weights to non-economic criteria. Third, the MCDA might provide a better framework for evaluating a landowner's selection of farming systems than the profit maximization model.