Question

A sporting goods store sells 300 hats in a season for $18 each. Each $1 increase in the price would result in five fewer hats being sold. Find the price of the hats to guarantee a revenue of $6625 from sales of the hats.

a) $19
b) $20
c) $21
d) $22

Answer 1

The price of the hats to guarantee a revenue of $6625 from sales of the hats is $21.

Step-by-step explanation:

To guarantee a revenue of $6625, we need to find the price of the hats that will result in selling the most hats. We can start by calculating the number of hats sold at different prices:

• At $18, 300 hats are sold.
• At $19, 300 - (1 * 5) = 295 hats are sold.
• At $20, 300 - (2 * 5) = 290 hats are sold.
• At $21, 300 - (3 * 5) = 285 hats are sold.
• At $22, 300 - (4 * 5) = 280 hats are sold.

We can see that as the price increases by $1, the number of hats sold decreases by 5. Now, we can calculate the revenue at different prices:

• At $18, the revenue is 300 * 18 = $5400.
• At $19, the revenue is 295 * 19 = $5605.
• At $20, the revenue is 290 * 20 = $5800.
• At $21, the revenue is 285 * 21 = $5985.
• At $22, the revenue is 280 * 22 = $6160.

To guarantee a revenue of $6625, the price of the hats should be $21. Therefore, the correct answer is c) $21.