The owner of a novelty store can obtain joy buzzers from the manufacturer for 50 cents apiece.He estimates he can sell 60 buzzers when he charges $1.00 apiece for them and that he will be able to sell 10 more buzzers for every 8 cent decrease in price.What price should he charge in order to maximize profit?
A)$0.79
B)$0.89
C)$1.09
D)$0.99

Question

Quizplus · Accepted Answer

Let's start by using the information given to form a table of possible prices, estimated sales, and estimated profit:

| Price | # of buzzers sold | Total revenue | Total cost | Profit |
|-------|------------------|---------------|------------|--------|
| $1.00 | 60               | $60.00        | $30.00     | $30.00 |
| $0.92 | 70               | $64.40        | $35.00     | $29.40 |
| $0.84 | 80               | $67.20        | $40.00     | $27.20 |
| $0.76 | 90               | $68.40        | $45.00     | $23.40 |
| $0.68 | 100              | $68.00        | $50.00     | $18.00 |
| $0.60 | 110              | $66.00        | $55.00     | $11.00 |
| $0.52 | 120              | $62.40        | $60.00     | $2.40  |

We can see that when the price is $1.00, the profit is $30.00, which is the highest profit in the table. So if the novelty store owner charges $1.00 apiece, he will maximize his profit.

However, the question asks for the price he should charge in order to maximize profit, taking into account the additional information that he will be able to sell 10 more buzzers for every 8 cent decrease in price. This means that we can continue the table to the left, with prices decreasing by 8 cents and estimated sales increasing by 10 for each row:

| Price | # of buzzers sold | Total revenue | Total cost | Profit |
|-------|------------------|---------------|------------|--------|
| $1.00  | 60               | $60.00        | $30.00     | $30.00 |
| $0.92  | 70               | $64.40        | $35.00     | $29.40 |
| $0.84  | 80               | $67.20        | $40.00     | $27.20 |
| $0.76  | 90               | $68.40        | $45.00     | $23.40 |
| $0.68  | 100              | $68.00        | $50.00     | $18.00 |
| $0.60  | 110              | $66.00        | $55.00     | $11.00 |
| $0.52  | 120              | $62.40        | $60.00     | $2.40  |
| $0.44  | 130              | $57.20        | $65.00     | -$7.80 |
| $0.36  | 140              | $50.40        | $70.00     | -$19.60|
| $0.28  | 150              | $42.00        | $75.00     | -$33.00|
| $0.20  | 160              | $32.00        | $80.00     | -$48.00|

We can see that the profit starts to decrease once the price drops below $0.76. Therefore, the highest price that will maximize profit is $0.76 + (1 * 0.08) = $0.84. However, we want to choose a price that is easier to work with, so we round up to the nearest penny and choose $0.85.

If the novelty store owner charges $0.85 apiece, he will be able to sell 90 buzzers, for a revenue of $76.50. His total cost will be $45.00 (90 buzzers at $0.50 apiece), leaving him with a profit of $31.50.

While this is not as high as the profit when charging $1.00 apiece, it is the highest profit for a price that takes into account the additional information given in the problem. Therefore, the best choice is:

Answer: D

The Owner of a Novelty Store Can Obtain Joy Buzzers