Question

A farmer produces wheat and soy in his farm of 250 acres. Each acre of wheat produced will earn him a revenue of $50 and each acre of soy will earn him a revenue of $65. Planting wheat incurs an expense of 40$ per acre and soy $50 per acre. The farmer must plant at least 10 acres of soy for every acre of wheat. The farmer has an initial amount of $25,000 for the work.

10. What can be the decision variables for the above LP(Linear Programing) problem?

1. initial expense of each wheat and soy
2. amount of profit of each wheat and soy
3. # of acres for each wheat and soy
4. not enough information to solve the problem

11. In the question above, what is the number of acres of wheat that should be planted?

1. 0
2. 150
3. 246
4. 46

12. in the problem above, what’s your advice to the farmer?

1. get more investment funds, if possible
2. get more land, if possible
3. both a and b
4. nothing can be changed

Answer 1

10). Answer is b). amount of profit of each wheat and soy.
Decision variable will depend on the amount of profit as profit is needed to be maximized.

11). Answer is a). 0
Wheat should not be planted on any acre of land as the profit per acre of soy is $15 i.e. ($65 - $50) which is higher than profit per acre of wheat i.e. $10 ($50 - $40). Also the required investment for soy is $50 * 250 acres = $12,500 while the available investment is much higher hence no scarecity.
If you solve through linear equation, you will get the number for soy acres only.

12). Answer is b). Get more land possible.
As the investment available is much higher than the required amount, farmer can get more land for making profit higher.