The owner of an orange grove must decide when to pick one variety of oranges. She can sell them for $18 a bushel if she sells them now, with each tree yielding an average of 7 bushels. The yield increases by half a bushel per week for the next 10 weeks, but the price per bushel decreases by $0.70 per bushel each week. When should the oranges be picked for maximum return?
A) 10 weeks from now
B) 2 weeks from now
C) 7 weeks from now
D) 5 weeks from now
E) 6 weeks from now

Question

The owner of an orange grove must decide when to pick one variety of oranges. She can sell them for $18 a bushel if she sells them now, with each tree yielding an average of 7 bushels. The yield increases by half a bushel per week for the next 10 weeks, but the price per bushel decreases by $0.70 per bushel each week. When should the oranges be picked for maximum return? ​​
A) 10 weeks from now
B) 2 weeks from now
C) 7 weeks from now
D) 5 weeks from now
E) 6 weeks from now

Quizplus · Accepted Answer

If the owner picks the oranges now, she will get 7 bushels per tree for $18 per bushel, making a total of 7 x $18 = $126 per tree.

If she waits one week, she will get an additional half bushel per tree, making the yield 7.5 bushels. However, the price per bushel will decrease by $0.70 to $17.30. This means the total return per tree is 7.5 x $17.30 = $129.75.

Continuing this analysis for each week, we get the following table:

Week	Yield per tree (bushels)	Price per bushel	Total return per tree
0	7	$18	$126
1	7.5	$17.30	$129.75
2	8	$16.60	$133.60
3	8.5	$15.90	$137.55
4	9	$15.20	$141.60
5	9.5	$14.50	$145.75
6	10	$13.80	$150.00
7	10.5	$13.10	$154.35
8	11	$12.40	$158.80
9	11.5	$11.70	$163.35
10	12	$11.00	$168.00

As we can see from the table, picking the oranges after 6 weeks will yield the maximum return per tree of $150. Therefore, the best choice is E) 6 weeks from now.

The Owner of an Orange Grove Must Decide When to Pick