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.
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.
Chapter5: Elasticity Of Demand And Supply
Section: Chapter Questions
Problem 1.1P: (Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of...
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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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