Question 32 - Linear Programming and variants We use resources to make products. Consider 6 such resources and 5 such products. Product Product 2 Product 3 Product Product 5 Profit of Product $510 $300 $510 $270 S810 2 10 2 3 6 Resource Availability 2487 3030 5217 6 3 6 3 10 2 3 10 6 2 Resource 1 Resource 2 Resource 3 Resource 4 Resource 5 Resource 6 7 6 $ 4 3 4000 5 6 3 10 2 4999 2769 10 3 5 3 4 1a) What is the optimal production plan (X1, X2, X3_X4,X5 ) and the associated profit? 1b) Suppose we now introduce the requirement that Product1, Product2 and Product 5 must be produced in equal amounts. Compared to the original feasible region (from part a), does adding this new requirement make the feasible region larger, stay the same, smaller, or something else? Clearly explain your answer. Also, what is the optimal amount to be produced of each of Producti, Product2, Product3, Product4, Products? And resultant profit? 1c) Returning to the original problem from part b, suppose we now introduce the additional requirement that Product1, Product2, Product 3, Product 4 and Product 5 must be produced in integer amounts, what is the optimal amount to be produced of each of Product1, Product2, Product3, Product4, Products? And resultant profit? 1d) Continuing on from part cabove, assume the same unit profits as before but now with fixed start-up costs as given below. Product Product 1 Product 2 Product 3 Product 4 Product 5 Unit Profit $510 $300 $510 $270 $810 Fixed-cost (Start-up cost) 2000 4000 8000 16000 1000 the optimal amount to be produced of each of Product1, Product2, Product3, Product4, Products? optimal value of the objective function