Question

A local restaurant recently began to offer an eat-in pizza promotion for their famous double-decker pizza. When priced at $17.99/person, the promotion attracted 112 customers per day on average. When they raised the price to $19.99/person they attracted an average of only 96 customers per day.

What price should the promotion be set at to generate the maximum daily profit?

Answer 1

the price that generates maximum profit is $152.94, rounded to the nearest cent.

Explanation:

Let's begin by finding the profit generated by the promotion at each price point.

At $17.99/person:

Profit = Revenue - Cost

Profit = $17.99 x 112 - (10 + 5 + 3) x 112

Profit = $2016.64

At $19.99/person:

Profit = Revenue - Cost

Profit = $19.99 x 96 - (10 + 5 + 3) x 96

Profit = $1497.12

To find the price that generates maximum profit, we need to use the formula:

Price = (Fixed Cost + Variable Cost) / Number of Customers + Profit per Customer

We can assume that the fixed cost for the restaurant is $10,000 per day, and the variable cost per person is $5 for ingredients and $3 for labor.

For $17.99/person:

Price = ($10,000 + (5 + 3) x 112) / 112 + ($2016.64 - $17.99)

Price = $152.94

For $19.99/person:

Price = ($10,000 + (5 + 3) x 96) / 96 + ($1497.12 - $19.99)

Price = $156.24

Therefore, the price that generates maximum profit is $152.94, rounded to the nearest cent.