Co points, 40 minutes) Consider the following resource allocation problem and the accompanying optimal tableau (s. Z. and Zy are slack variables). (Profit 5) (Resource 1) maximize z = 15x + &ry + 10 +1264 subject to *+213 + x 520 *+ x2 + 3+ 4554 + 2xy + x3 + x 5 36 11, 12, 13, 420 (Resource 2) (Resource 3) Z X 23 4 As X X2 RHS z 1 9 0 0 2 4 0 10 440 0 0 0 1 0 0 -1 0 1 0 1 0 0 -1 1 10 8 36 23 2 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? (3 points) b) For what values of c3 .objective function coefficient as the basis remains optimal? (5 points) What would be the new optimal solution if og reduces from 10 to 67 (10 points) c) Suppose a new product is proposed with an objective coefficient 16. Assume production of one unit of this new product requires 1.1 and 1 units of resources 1. 2. and 3 respectively. Use 2 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)