4-25. A gardener has 1,000 square yards of land available to devote to cash crop

Question

4-25. A gardener has 1,000 square yards of land available to devote to cash crops. Profits expected by crop are: $20 per square yards for lima beans, $10 per 10 square yards for spinach, and $15 per 10 square yards for zucchini. The gardener has $200 available for investment. Total preparation cost for 10 square yards are $4 for lima beans, $2 for spinach, and $1 for zucchini. The gardener has 200 hours available for gardening. Each 10 square yards requires 2 hours for lima beans, 1 hour for spinach, and 3 hours for zucchini.

a. Formulate a linear programming model to determine the optima areas in square yards for each of the three crops.

Explanation / Answer

Answer:

x sq yards of lima beans

y sq yards of spinach

z sq yards of zzucchini

The objective function is:

Maximize profit = P = $20x + $y + $1.5z

Constraints are:

400x + 200y + 100z<=200

40x + 20y + 60z <= 200

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