An investor has 125 acres and has $ 40,000 stock for investment. Each member can provide 3500 hours of work during the winter and 4000 hours during the summer. If any of these hours are not necessary then the younger members of the family can go and work in the nearby farm for birr 5 per hour for the winter months and birr 6 per hour during the summer. Income in cash can come from the three crops, from cows and from chickens. No stock investment is needed for crops. In contrary an investment of birr 1200 for each cow and birr 9 for each chicken is needed.

Each cow needs 1.5 hectares of land, 100 labour hours of personal work during the winter months and another 50 hours for the summer. Each cow will give income birr 1000 each year for the family. The corresponding figures for each chicken is no land, 0.6 hours of personal human work in winter and 0.3 more hours in summer with annual income birr 5 for each chicken. The farm can feed a maximum of 3000 chickens and the existing stable is sufficient for up to 32 cows. The estimated hours of personal work and the income per cultivated hectare for the three types of crop are the following:

Soya Corn Oat

Winter hours 20 20 20

Summer hours 50 50 50

Net annual income ($) 500 500 500

The family wants to determine how much land should be cultivated for each crop type and how many chickens and cows should be kept to maximize the annual net profit. Design a linear programming model to solve this problem.

Required:

a)Formulate the above problem as a linear programming model

b)Solve the problem using simplex method.