A farmer has 1200 acres of land and plans 10 plant corn and soybeans. The input cost (cost of seed, fertilizer, herbicide, and insecticide) for 1 acre or each crop is given in the table along with the cost of machinery and labor. The profit for 1 acre of each crop is given in the last column.
Input Cost per Acre | Labor/Machinery Cost per Acre | Profit per Acre | |
---|---|---|---|
Corn | $180 | $80 | $120 |
Soybeans | $120 | $100 | $1000 |
Suppose the farmer has budgeted a maximum of $198,000 for input costs and a maximum of $110,000 for labor and machinery.
a. Determine the number of acres of each crop that the farmer should plant to maximize profit. (Assume that all crops will be sold.)
b. What is the maximum profit?
c. If the profit per acre were reversed between the two crops (that is, $100 per acre for corn and $120 per acre for soybeans), how many acres of each crop should be planted to maximize profit?
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College Algebra (Collegiate Math)
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