11. 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 ql and the off-peak demand is given by p2 = 380 qz, where q; is the units of power demanded and pi is the price for each unit of power in each market. The variable cost is 20 per unit of power [paid in both markets}. Capacity costs 113 per unit and is only paid once and used in both periods. {a} Write down the Lagrangian and constraints to maximize profit. {b} Find the optimal outputs and capacity for this