(30 points, 40 minutes) Consider the following resource allocation problem and the accompanying 5. 36, and 2y are slack variables) Time left 1:36:21 maximize z = 15x7 + 8x2 + 10xz + 12x4 (Profit $) subject to xy + 2x2 + x4 = 20 (Resource 1) (Resource 2) x1 + x2 + x + x 4 = 54 2x1 + x3 + x = 36 (Resource 3) X1, X2, X3, X4 20 2 X1 X2 X3 X4 Xs X6 X7 RHS 1 9 0 0 2 4 0 z 10 440 1 X2 1 - 2 0 0 0 -- 1 0 0 0 0 1 NeoN X6 0 1 0 - 0 0 -1 1 10 8 36 1 X3 ZX1 X2 X3 X4 X's X6 X7 RHS N 1 9 0 0 2. 4 0 10 440 X2 1 0 X6 OOO 0 - 2 NON- 1 0 0 0 0 1 - -11 10 8 36 X3 1 0 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 first, and why? (6 points) b) Suppose that the coefficient of 21 in the objective function changes from 15 to 30. What would be the new optimal solution? (12 points) c) Suppose a new product is proposed with an objective coefficient of 30. Assume production of one unit of this new product requires 4, 5, and 1 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)