Question

You are thinking of building a restaurant on Cape Cod. The marginal cost of building the restaurant is equal to $10 per​ diner, and the marginal cost of an additional meal is $20 per diner. In the peak vacation​ period, the weekly demand function​ is:

QPEAK=$4,200−40P PEAK.

In the​ off-peak period, the weekly demand function​ is:

Q OFF−PEAK=$1,800−20P OFF−PEAK.

P is the price of a meal.

The​ profit-maximizing quantity of meals during the peak vacation period is _____.

The​ profit-maximizing price of a meal during the peak vacation period is $_____

The​ profit-maximizing quantity of meals during the​ off-peak vacation period is _____.

The​ profit-maximizing price of a meal during the​ off-peak vacation period is $_____

Answer 1

QPEAK = 4200 -40P

OR P = 105 - 0.025Q

Q OFF PEAK = 1800-20P

OR P = 90 - 0.05Q

TR PEAK = 105Q - 0.025Q²

MR PEAK = 105 - 0.05Q

MC = 20

105 -0.05Q = 20

Q=1700

P = $62.5

The​ profit-maximizing quantity of meals during the peak vacation period is 1700

The​ profit-maximizing price of a meal during the peak vacation period is $62.5

TR NON PEAK = 90Q - 0.05Q²

MR NON PEAK = 90 - 0.1Q

MC = 10

90 -0.1Q = 10

Q = 800

P = $50

The​ profit-maximizing quantity of meals during the​ off-peak vacation period is 800.

The​ profit-maximizing price of a meal during the​ off-peak vacation period is $50.