Question

A resort sells an all-included package for a week-long stay at $2000 per person. It costs $1600 for the resort to operate, so the profit is $400 per package. They sell 300 packages every month. The resort wants to increase the price and they estimate that the number of packages sold will decrease by 5 every time they increase the price by $100. What price will maximize the monthly profit? Find the maximal profit, the number of packages, and their price to get that profit.

Answer 1

To find the price that will maximize the monthly profit, we need to determine the profit for each price and find the maximum profit.

Step-by-step explanation:

To find the price that will maximize the monthly profit, we need to determine the profit for each price.

Let's start by finding the profit for the current price of $2000 per package:

Profit per package = Revenue per package - Cost per package

Profit per package = $2000 - $1600 = $400

Next, let's determine the profit for a higher price. For each $100 increase in price, the number of packages sold will decrease by 5.

To find the new price that maximizes the profit, we need to find the price where the revenue per package is equal to the cost per package.

Using the equation Profit per package = Revenue per package - Cost per package, we can calculate the profit for each price and find the maximum profit: