# Maximizing Profits - Demand and Marginal Revenue Curves

The (inverse) demand curve for the services of Oakland Pest Control Co. (OPCC) is given by

P = $1000 - 2Q, where P is in dollars, and Q is residences/month.

The cost equation is given by C = 2000 + 30Q.

a. Sketch and label OPCC's demand and marginal revenue curves, and determine the maximum revenue it can make.

b. What are OPCC's profit-maximizing price and output levels?

c. How much profit does OPCC make if it services 100 residences per month?

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#### Solution Preview

a.

Demand curve:

P = 1000 - 2Q

Total Revenue (TR) = PQ

TR = (1000 - 2Q)Q

TR = 1000Q - 2Q^2

MR is the derivative of TR:

MR = 1000 - 4Q

See the attached file for the ...

#### Solution Summary

This solution shows how to find the Quantity and Price that maximizes the profits of Oakland Pest Control when the firm's Demand Curve and Total Cost Curve are known.