Joe "Mr Clean" Smith Is Planning to Start a New Service

Essay

Joe "Mr. Clean" Smith is planning to start a new service for his car wash company. Previously, everyone who wanted their car washed had to come to Joe's business Mr. Clean Car Wash. He and his staff have decided that there is a substantial market for people who would want to have their car washed at their home. After considerable, and I might add free, market research performed by the Small Business Development Center of the University of Texas at San Antonio, the following daily demand equations have been determined.
The estimated demand for car washes done at Mr. Clean is given by the following equation:
Q_c = 550 - 25P_c, so that MR_c = 22 -.08Q_c
The estimated demand for car washes done at home is given by the following equation:
Q_h = 95 - 2.5P_h, so that MR_h = 38 - .8Q_h,
where Q_c is the number of car washes per day done at Mr. Clean and Q_h is the number of cars washes done at people's homes. Because he is only sending one person out to do the cars washes at home and he does not have to pay for water, Joe estimates that the marginal cost for both in-house and at-home car washes to the same and is constant at $6.00
a. Should the price for picked up in-house car wash be lower than the price for the at-home one?
b. How many car washes should be sold in each market to maximize profit?
c. What price or prices should be charged each type of customer?