Problem 5. (20 points) Consider the following resource-allocation problem and accompanying optimal tableau (rs, x6, and x7 are the respective slack variables) (Profit S) (Resource 1) (Resource 2) (Resource 3) maximize 15xi +8x2 + 10 x3 - 12x4 subject to xi 2x2 +x4 20 2x xi, x2, 3, x42 0 -26 1/2 RHS 440 10 -4 -10 1/2 0 3/2 1/2 36 5 points each) a) Write the dual problem and specify the optimal dual solution from the foregoing tableau b) What are the shadow prices of the resources? If you were to choose between increasing the amount of resources 1,2, or 3, which would you choose to increase and why? c) Suppose that the coefficient of x4 in the objective function changes from (12) to 20. Using sensitivity analysis, find the new optimal solution. Suppose that the available amount of resource 1 changes from 20 to 40. Using sensitivity analysis, find the new optimal solution d) Problem 5. (20 points) Consider the following resource-allocation problem and accompanying optimal tableau (rs, x6, and x7 are the respective slack variables) (Profit S) (Resource 1) (Resource 2) (Resource 3) maximize 15xi +8x2 + 10 x3 - 12x4 subject to xi 2x2 +x4 20 2x xi, x2, 3, x42 0 -26 1/2 RHS 440 10 -4 -10 1/2 0 3/2 1/2 36 5 points each) a) Write the dual problem and specify the optimal dual solution from the foregoing tableau b) What are the shadow prices of the resources? If you were to choose between increasing the amount of resources 1,2, or 3, which would you choose to increase and why? c) Suppose that the coefficient of x4 in the objective function changes from (12) to 20. Using sensitivity analysis, find the new optimal solution. Suppose that the available amount of resource 1 changes from 20 to 40. Using sensitivity analysis, find the new optimal solution d)