Question

A store sells portable MP3 players for $100 each and, at this price, sells 120MP3 players every month. The owner of the store wishes to increase his profit, and he estimates that, for every $2 increase in the price of MP3 players, one less MP3 player will be sold each month. If each MP3 player costs the store $70, at what price should the store sell the MP3 players to maximize profit?

Answer 1

To maximize profit, the store should sell the MP3 players for $102.

Step-by-step explanation:

To maximize profit, the store needs to find the price that will generate the most revenue. We can start by calculating the revenue at the current price of $100: 120 MP3 players * $100 = $12,000. Next, we can determine the number of MP3 players that will be sold for every $2 increase in price: 1 less MP3 player sold for every $2 increase. Therefore, for every $2 increase, the revenue will decrease by $100. To find the price that maximizes profit, we need to subtract the cost of each MP3 player from the revenue and then choose the price that results in the highest profit.

Let's start by calculating profit at the current price:

Profit = (Revenue - Cost)

Profit = ($12,000 - (120 MP3 players * $70))

Profit = ($12,000 - $8,400) = $3,600

Now, let's calculate profit for an increase in price of $2:

Profit = (Revenue - Cost)

Revenue = (119 MP3 players * ($100 + $2)) = $12,078

Profit = ($12,078 - (119 MP3 players * $70))

Profit = ($12,078 - $8,330) = $3,748

By comparing the profits at different price points, we can determine the price that maximizes the profit. In this case, the price that maximizes profit is the one that results in the highest profit. From the calculations, we can see that an increase in price of $2 results in a higher profit. Therefore, the store should sell the MP3 players for $102 to maximize profit.