A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number of laundry sinks demanded and p is the price of a laundry sink. (1) If we assume that the total cost per day is linearly related to the number of sinks produced in a day, derive the total cost function of the company? (2) Find a function for the average cost of this company. (3) If production increases continuously, what is likely to be the average cost per sink? (4) How many laundry sinks will the company need to produce in order to maximise it′s profits? (5) What is the maximum profit?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 6SC: A company that makes and sells baseball caps has found that the total monthly cost C in dollars of...
Question

A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number of laundry sinks demanded and p is the price of a laundry sink.

(1) If we assume that the total cost per day is linearly related to the number of sinks produced in a day, derive the total cost function of the company?

(2) Find a function for the average cost of this company.

(3) If production increases continuously, what is likely to be the average cost per sink?

(4) How many laundry sinks will the company need to produce in order to maximise it′s profits?

(5) What is the maximum profit?

 

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