LESSON 3

Optimization Techniques

Activity 3 Case 2

1. Assume that the firm's cost function is given by TC = 30 + 5Q + Q 2 where, Q is the level of output produced and sold,

Assume further that the demand for the output of the firm is a function of price P given by the relationship

Q = 20 - P

A. Define the total profit function as the difference between total revenue and total cost, expressed in terms of Q the total profit function for the firm.

B. Determine the output level where total profits are maximized.

C. Calculate total profits and selling price at the profit-maximizing output level.

2. Mags, Inc. has determined through regression analysis that its sales (TR) are a function of the amount of advertising (measured in units) in two different media. This is given by the following relationship (X = newspapers, Y = magazines):

TR = 300X + 100Y - 10X2 - 20Y2 + 20XY

A. Determine the level of newspaper and magazine advertising that maximizes sales subject to this budget constraint.

B. Calculate the firm's sales at this constrained optimum level.