a) A car tire company produces and sell 3 tires (t) for 1 frame (f). The demand function for t is t=66 - 0.5Pt and the demand function for f is f=63 -pf. The total cost of the firm is: TC-t2 + tf + f2 + 45. Use the Lagrange Multiplier method of constrained optimization optimize the profit, and find all the optimal values. b) Now use the Bordered Hessian method to show that all the optimal values that you find in (a) maximize the profit. c) Define the significance of Lagrange Multiplier in optimization using this context. What is the other name of Lagrange Multiplier? Please briefly discuss how it will affect a firm's decision in this context?