(30 points, 40 minutes) Consider the following resource allocation problem and the accompanying optimal tableau (xs. X, and sy were slack variables). maximize z 15x + xy + Nay + 124 (Prodit subject to 4+27+45 20 (Resource 1) x + x + y + x4554 (Resource 2) 2x + xy + 45 36 (Resource 3) Z 2 RHS X1 X2 I) I's 14 X 1 9 0 Z 0 4 0 10 440 1 4 1 0 0 0 0 0 x -1 2 1 0 0 -1 1 10 8 36 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 c) , abjective function coefficient xy, the basis remains optimal? (5 points) What would be the new optimal solution if y reduces from 10 to 6? (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 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)