Question 1 (25 points) Consider a production line with four workstations, labeled j = 1,2,3,4 in tandem (all products flow through all four machines in order). Three different products, labeled i = A.B.C are produced on the line. The hours required on each workstation for each product and the net profit per unit sold (ri) are given as follows: i A B 1 2 3 4 2.4 1.1 0.8 3 2 2.2 1.2 2.1 0.9 0.9 1 2.5 50 65 70 The number of hours available (Cje) and the forecasted demand, denoted by die for each product over the next four quarters are as follows: t 1 2. 3 4 640 640 1280 GE Car 640 1280 640 1920 1280 640 1920 1280 Car Cat 640 1920 2560 dar 1920 1280 50 120 250 100 20 300 75 50 20 250 da 25 400 a. For a quarterly holding cost of $5 and a quarterly backlog cost of $10 per item on all products and allowed backordering, formulate an LP to maximize profit minus holding and backorder costs subject to the constraints on workstation capacity and minimum and maximum sales. (8 pnts) b. Solve the same problem for holding costs of 10 and 15. How does your results change? 17 pnts) c. Due to some error, the production planner realizes that they underestimate the backlog by 50% (berue = 20). Provide an algorithm that calculates the holding cost rate that yields the closest production orders to the mistaken backlog cost rate (b = 10). Only provide a pseudo-code. Do not solve the problem. (10 pnts)