A Farmer Has 150 Acres of Land Suitable for Cultivating

question 45

Multiple Choice

A farmer has 150 acres of land suitable for cultivating crops A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $7,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 3,300 labor-hours available. If he expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should he plant in order to maximize his profit? What is the largest profit the farmer can realize? Are there any resources left over?

• A) 65 acres of crop A, 80 acres of crop B; maximum profit $25750; $0 left over, 5 acres of land left over, 0 labor-hours left over
• B) 150 acres of crop A, 80 acres of crop B; maximum profit $51,000; $2,200 left over, 0 acres of land left over, 0 labor-hours left over
• C) 90 acres of crop A, 60 acres of crop B; maximum profit $51,000; $200 left over, 0 acres of land left over, 0 labor-hours left over
• D) 150 acres of crop A, 0 acres of crop B; maximum profit $22,500; $2,200 left over, 0 acres of land left over, 300 labor-hours left over

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Definitions:

Utility from Insurance

The satisfaction or utility gained by individuals from reducing uncertainty and risk in their lives through the purchase of insurance contracts.

Income Increase

Income increase refers to the rise in an individual's or household's earnings, affecting their purchasing power and consumption habits.

Fair Insurance Policy

An insurance policy for which the premium is equal to the expected value of the claim.

Risk-Averse

The characteristic of preferring to avoid risk, opting for lower but more certain returns over potential higher but uncertain returns.