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Sagot :
9514 1404 393
Answer:
4 acres of each
Step-by-step explanation:
Let s and c represent the number of acres of soybeans and corn, respectively. The problem statement gives rise to several constraints. There is also an objective function to maximize. The linear programming problem can be described by ...
maximize 500s +300c subject to ...
s ≥ 2
200s +100s ≤ 1200 . . . . cost to plant
s + 2c ≤ 12 . . . . . . . . . . . . hours to plant
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The attached graph shows the objective function is maximized at (s, c) = (4, 4).
The farmer should plant 4 acres each of soybeans and corn.
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For the solution here, the constraint that s ≥ 2 is irrelevant. If the graph included it, the vertices of the feasible solution space would be (2,5), (4, 4), (6, 0) and (2, 0). The solution that maximizes profit is (4, 4).

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