21. A farmer has 1,000 acres of land on which he intends to plant corn, wheat and soyabeans. Each acre of corn costs Rs 10,000 for preparation, requires 7 worker days of labour, and yields a profit of Rs 3,000. An acre of wheat costs Rs 12,000 to prepare, requires 10 worker days of labour, and yields Rs 4,000 profit. An acre of soyabeans costs Rs 7,000 to prepare, requires 8 worker days of labour, and yields Rs 2,000 profit. The farmer has taken out a loan of Rs 80,00,000 for crop preparation and has contracted with a union for 6,000 worker days of labour.

A granary has agreed to purchase 200 acres of corn, 500 acres of wheat and 300 acres of soyabeans. The farmer has established the following goals, in order of their importance:

(i) In order to maintain good relations with the union, the labour contract must be honoured;

that is, the full 6,000 must be used.

(ii) Preparation costs should not exceed the loan amount so that additional loans will not have to be secured.

(iii) The farmer desires a profit of at least Rs 1,05,00,000 in order to remain in good financial condition.

(iv) Contracting for excess labour should be avoided.

(v) The farmer would like to use as much of the available acreage as possible.

(vi) The farmer would like to meet the sales with the granary. However, the goal should be weighted according to the profit returned by each crop.

Formulate a goal programming model for determining the number of acres of each crop the farmer should plant in order to satisfy the goals in the best possible way.

(MBA, Delhi, March 2003)