Homework SourseWalnut Orchard has two farms that grow wheat and corn Becaus
Walnut Orchard has two farms that grow wheat and corn. Because of different soil conditions, there are differences in the yields and costs of growing crops on the two farms. The yields and costs are sown in the table below. Each farm has 100 acres available for cultivation; 11,000 bushels of wheat and 7,000 bushels of corn must be grown. Use Linear Programming to determine a planting plan that will minimize the cost of meeting these demands.(use the simplex method)
| Farm 1 | Farm 2 | |
| Corn yield / acre (bushels) | 500 | 650 |
| Cost / acre of corn ($) | 100 | 120 |
| Wheat yield / acre (bushels) | 400 | 350 |
| Cost/ acre of wheat ($) | 90 | 80 |
Solution
Decision Variable
C1 = No. of acres of Farm 1 planted in corn
W1 = No. of acres of Farm 1 planted in wheat
C2 = No. of acres of Farm 2 planted in corn
W2 = No. of acres of Farm 2 planted in wheat
Constraints
• Restrictions of the number of acres of each farm which are planted in crops.
C1 + W1 100
C2 + W2 100
• Restrictions of the minimum quantity of each crop.
500C1 + 650C2 7000
400W1 + 350W2 11000
• Non-negativity constraint on each of the four variables.
C1 0 C2 0, W1 0, W2 0
Objective:
Minimize 100 C1 + 120C2 + 90 W1 + 80 W2
Linear Programming Formulation
MIN 100 C1 + 120C2 + 90 W1 + 80 W2
SUBJECT TO
C1 + W1 100
C2 + W2 100
500C1 + 650C2 7000
400W1 + 350W2 11000
