Can you solve the a, b and c seperately?

(30 points, 40 minutes) Consider the following resource allocation problem and the accompanying optimal tableau ( X5, X6, and xy are slack variables). maximize z = 15x + 8x2 + 10xz + 12x4 (Profit ) subject to xy + 2x2 + x = 20 X1 + x2 + x3 + x 54 2x1 + x3 + x 5 36 X1, X2, X3, X4 20 (Resource 1) (Resource 2) (Resource 3) Z X1 X2 X3 X4 X's X9 RHS Z 11 9 0 2 2 4 0 10 440 - 1 0 0 0 - -1 X6 X3 - 2 0 0 -- 0 10 8 36 0 - a) What are the shadow prices (duals) of the resources? If you were to choose between increasing the amount of resource 1, 2 or 3, which would you choose to increase, and why? (6 points) b) Suppose that the coefficient of Xs in the objective function changes from 12 to 16. What would be the new optimal solution?(12 points) c) Suppose a new product is proposed with an objective coefficient 16. Assume production of one unit of this new product requires 1, 2, and I units of resources 1, 2, and 3 respectively. Use Xo to refer to the new product. What would be the new optimal solution (values of the decision variables and the objective function value) after the introduction of the new product? (12 points)