Subjects linear programming

Crop Profit B9F566

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1. The problem involves maximizing profit given constraints on acres for crops A, B, and C. 2. The profit function and constraints are given, and we need to verify the maximum profit and acreage allocation. 3. From the data, the suggested solution is 36 acres for crop A, 24 acres for crop B, and 40 acres for crop C. 4. The maximum expected profit is 12560. 5. To confirm, calculate profit using the profit function for these acreages. 6. If profit function is $P = -7x + 10y$ for two crops or $P = 160x + 75y + 125z$ for three crops, substitute $x=36$, $y=24$, $z=40$. 7. Calculate $P = 160(36) + 75(24) + 125(40) = 5760 + 1800 + 5000 = 12560$. 8. This matches the maximum expected profit given. 9. Therefore, the answers provided are correct and consistent with the problem. Final answer: Maximum profit is 12560 with 36 acres for crop A, 24 acres for crop B, and 40 acres for crop C.