1. For the linear program: Max 2A + 3B s.t. A + B 12 Constraint "1" A + 2B 16 Constraint "2" -3A + 2B 6 Constraint "3" A, B 20 Should be done manually (must show hand work). a. Making "A" as the horizontal variable, graph the problem neatly. Show the feasible region. Label constraints on graphs. b. Solve the problem. Show work. What is the optimal "A" and "B" values? What is the optimal objective function value? c. What are the values of slack and surplus for each constraint? d. Holding the coefficient of "B" in the objective function fixed, how much can the coefficient of "A" decrease or increase so that the optimal solution does not change? e. Holding the coefficient of "A" in the objective function fixed, how much can the coefficient of "B" decrease or increase so that the optimal solution does not change? f. Suppose the coefficient of "A" changes from 2 to 3 and the coefficient of "B" changes from 3 to 2. Will the optimal solution change? If so, what is the new optimal solution? g. Which constraints have non-zero shadow prices? Explain. h. Find the shadow price for constraint "1" by hand (that is, show the algebra and computations).