hssignment 5: Linear Programming Submission date: 9 October 2024 All problems are fictitious. No other data accompanies this assignment. QUESTION 1: 15 marks The Southcal Garment Company is developing next year's business plan for their factory. The company makes two lines of children's clothes, the Bobby line and the Charlie line. The Bobby line takes more handwork but is more profitable. Production is labor-intensive and because of its agreement with the Southern California Employment District, Southcal cannot hire anymore workers. Bobby line averages about $1800 profit per 100 garments and Charlie line averages about $1000 per 100 garments. The cutting departmenthas 36,000 cutting hours available next year and 100 garments of the Bobby line takes 4 hours of cutting labor and 100 garments of the Charlie line takes 2 hours of cutting labor. The sewing department has 60,000 labor hours available for next year and for 100 garments of the Bobby line, 6 hours of sewing labor is required and for 100 garments of the Charlie line 4 hours of sewing labor is required. Southcal Garment Company's question is how many units of each product line should be included in next year's business plan to maximize the profit? 1) State the objective function to be solved and give descriptions to the decision variables. 2) State the constraints that determine the boundaries within which this problem should be solved. 3) Present this problem graphically, and clearly identify the feasible region on the graph. 4) Identify the optimalsolution for this problem and word a recommendation to SouthCal Garment Company's question. QUESTION 2: 15 marks MadeRite, a manufacturer of paper stock for copiers and printers, produces cases of finished paper stock at Mills 1, 2, & 3. The paper is shipped to Warehouses A, B, Cand D. The shipping cost per case, the monthly warehouse requirements and the monthly mill production levels are: Destination Monthly Mill A B C D Production Capacity (cases) Mill 1 $6.20 $4.10 Mill 2 $7.10 $5.60 Mill 3 $5.20 $5.50 Monthly Warehouse Requirement (cases) 9,000 12,000 1) State the objective function to be solved and give descriptions to the decision variables. 2) State the constraints that determine the boundaries within which this problem should be solved. 3) Setup this problem and use a SOLVER to solve this problem. 4) How many cases of paper should be shipped per month from each mill to each warehouse to minimize the shipping costs