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texas101st78
18.01.2021 •
Mathematics
A farmer is going to divide her 30 acre farm between two crops. Seed for corn costs $15 per acre. Seed for wheat costs $30 per acre. The farmer can spend at most $750 on seed.If wheat brings in a profit of $110 per acre, and corn brings in a profit of $100 per acre, how many acres of each crop should the farmer plant to maximize her profit
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Ответ:
$3200
Step-by-step explanation:
The total area of land is 30 acre. Let x represent the area in acre that corn is planted and y represent the area in acre that wheat is planted. Therefore:
x + y = 30 (1)
Also, the farmer can spend at most $750 on seeds. Corn cost $15 per acre, maize cost $30 per acre. Hence:
15x + 30y ≤ 750 (2)
Also, x and y > 0
The profit is given by the function:
Profit = 100x + 110y
Graphing equation 1 and equation 2 and solving, we get the points:
(10, 20)
Hence the maximum profit is at:
Max profit = 100(10) + 110(20) = $3200
Ответ: