Answer to Question #119701 in Microeconomics for Rosi

Question

A firm produces cellular telephone service using equipment and labor. When it uses E machine-hours of equipment and hires L person-ours of labor, it can provide up to Q unites of telephone service. The relationship between Q, E, and L is as follows: Q = EL . The firm must always pay PE for each machine-hour of equipment it uses and PL for each person-hour of Labor it hires. Suppose the production manager is told to produce Q=200 units of telephone service and that she wants to choose E and L to minimize costs while achieving that production target.
a) What is the objective function for this problem?

Answer 1

$$Q=pE\times PL$$

$$Q=p^2 \times EL$$