1. Kuhn Tucker Theorem Problem

An electric company is setting up a power plant in a foreign country and it has to plan its capacity.

The peak period demand for power is given by P1 = 400 - Q1 and the off-peak is given by P2 =

380 - Q2. The variable cost is 20 per unit (paid in both markets) and capacity costs 10 per unit

which is only paid once and is used in both periods.

a. Set up the economic problem of peak-load pricing above by stating what the objective

function and constraints are!

b. Write out the Kuhn-Tucker conditions for this problem!

c. Find the optimal outputs (Q1,Q2) and capacity (K) for this problem!

d. How much of the capacity is paid for by each market (i.e. what are the values of 1 and 2)?