6. A monopolist produces three different products at three plants with respective costs: C1 = Q1 + Q3 C2 = 3Q2 63 = 3Q3 - Q3 The inverse demand for the products: P1 = 30 - Q1 P2 = 50 - Q2 P3 = 40 - Q3 a. Find the critical values of the firm's profit: (q1,q2, q3, pi, pz, p3, n*) [Hint: First, find the equation for revenue then find the equation for profit.] b. Use the Hessian method to classify each point as a local maximum, local minimum or indeterminate (saddle point). 7. Suppose you purchase a zero-coupon bond ( a bond that does not pay any interest until maturity) that has a face value of $25,000 in 20 years. Assuming a continuous compounding rate of 7% and no administrative costs, how much should you pay for the bond? [Hint: think of this as a discounting (negative growth rate) from 20 years to today.]