Suppose earnings are given by E = $60 + $7(24 − L),where E is earnings and L is the hours of leisure.What is the maximum this worker can earn in three (3)days?
A) $519
B) $417
C) $228
D) $684

Question

Quizplus · Accepted Answer

To maximize earnings over three days, we need to find the optimal amount of leisure time that achieves the highest earnings.

Since the worker is given 24 hours in a day, the maximum amount of leisure time the worker can take per day is 24-L.

To maximize earnings, we need to find the amount of leisure time that maximizes E.

Taking the derivative of E with respect to L:

dE/dL = -7

Setting the derivative equal to 0:

-7 = 0

This implies that there is no maximum or minimum point and earnings decrease as the worker takes more leisure time.

Therefore, the worker should work for all 72 hours over three days, earning:

E = 60 + 7(24-0) = $684

Thus, the answer is D.

Suppose Earnings Are Given by E = $60 + $7(24