– A certain cleaning company cleans professional offices and believes its staff can clean up to 300 office units a week at a labor and supply cost of $58 per unit. Preliminary pricing surveys indicate that if that if the company charges $100 per unit, it will have clients for 300 units. For every $5 price increase it can expect a demand of 10 fewer units. Assume the demand, s, is a linear function of price p. Find an equation for demand as a function of price. Find the Revenue and Cost functions, both of which are dependent on price p. Write the Profit function. Using Desmos, graph the Revenue, Cost, and Profit functions on the same coordinate plane. Label the axes and the functions and use an appropriate scale.Find the break-even points graphically and confirm algebraically. Label the regions of profit and loss on the graph.Algebraically find the price that results in a maximum profit.Conclusion:A price of $_________ results in a quantity of _____________ units cleaned, which yields a maximum profit of $___________________.Include the Desmos graph.

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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– A certain cleaning company cleans professional offices and believes its staff can clean up to 300 office units a week at a labor and supply cost of $58 per unit. Preliminary pricing surveys indicate that if that if the company charges $100 per unit, it will have clients for 300 units. For every $5 price increase it can expect a demand of 10 fewer units.

Assume the demand, s, is a linear function of price p. Find an equation for demand as a function of price.

Find the Revenue and Cost functions, both of which are dependent on price p.

Write the Profit function.

Using Desmos, graph the Revenue, Cost, and Profit functions on the same coordinate plane. Label the axes and the functions and use an appropriate scale.
Find the break-even points graphically and confirm algebraically. Label the regions of profit and loss on the graph.
Algebraically find the price that results in a maximum profit.
Conclusion:

A price of $_________ results in a quantity of _____________ units cleaned, which yields a maximum profit of $___________________.

Include the Desmos graph.

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