QUESTION THREE (20 MARKS) a) A farmer has 300 hectares of land on which to grow maize, wheat and…

QUESTION THREE (20 MARKS)

a) A farmer has 300 hectares of land on which to grow maize, wheat and beans. He intends to spend no more than £8000 and it requires £20 to cultivate one hectare of maize, £ 20 to cultivate one hectare on wheat and £40 to cultivate one hectare of beans. He has a workforce of 600 laborers and their requirement is 2 for each ha on maize, 1 for each ha on wheat and 3 for each ha on beans. The profit contributions of the three crops are £25, £30 and£35 per ha respectively and the farmer wishes to maximize the profit. Formulate this problem as a linear programming problem and solve it using simplex method

[17 Marks]