Question

Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.

Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.

Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that x represents the number of $1 increases in the cost of the buffet.

Enter the correct answer in the box. Type the cost expression on the first line and the customer expression on the second line.

Answer 1

The best pricing decision that is made is to sell each unit for $3.

How to calculate the price?

From the information given, the revenue will be:

= Customer × Charge

= 16 × 10

= 160

Based on the information given, the equation will be:

(10 + x)(16 - 2x) ≥ 130

160 - 20x + 16x - 2x² ≥ 130

-2x² - 4x + 30 ≥ 0

x² + 2x -15 ≤ 0

(x+1)² ≤ 4²

x+1 ≤ 4

x ≤ 3

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