The Rowling Company manufactures three types of men's coats: sporty, formal, and executive. The 3 lines of coats are manufactured in two departments. the amount of material for one of the bags, as well as the time in each department is shown in the following table. The profit contribution of each shelter is USD 150, 200 and 280 respectively. Management has forecast that market demand for the sports coat is 1000 units per week and orders for the other two lines are 500 and 200. Product requirements per unit Sport Formal Executive Available Resources Department 1 4 hours 12 hours 10 hours 8000 hours Department 6 hours 6 hours 16 hours 5000 hours 2 Material 6 yds 6 yds 12 yds 8 yds Administrators have established the following goals: Objective 1: Use all available production capacities, there should be no dead time in department 1 and 2, that is, use at least the available hours. Objective 2: Achieve a profit goal of 100,000. Objective 3: Satisfy all market demand, that is, at least 1,000 sports, 500 formal and 200 executive jackets must be manufactured. a) State the problem as programming by goals. b) Solve the problem in POM and draw conclusions. c) The company has established priorities that objective 3 has the highest priority, followed by profits, and priority 3 to use all the time of the departments. Set the objective function, solve and draw conclusions. b) Solve the problem in POM and draw conclusions. M QM for Windows V5 (untitled) W(d+) Prty(d+) Wid-) Prty(d-) X1 x2 x3 RHS Goal/Cnstrat 1 4 12 10 8000 Goal/Cnstrat 2 0 0 6 6 16 5000 Goal/Cnstrnt 3 1 0 100 Goal/Cnstrat 4 0 0 0 1 0- 50 Goal/Cnstrat 5 0 0 1= 50 Goal/Cnstrat 6 0 0 0 0 B 6 12- Goal/Cnstrat 7 0 30 70 150 = 100000 Goal/Cnstrat 8 0 0 1 0 0- 1000 Goal/Cnstrat 9 0 0 0 0 1 0 = 500 Goal/Cnstrat 10 0 0 1 200 Summary (untitled) Solution nem a Decision variable analysis Value X1 0 x2 181.82 X3 581.82 Priority analysis Nonachiev Constraint Analysis RHS d+ (row) d-(row ) Goal/Cnstrnt 1 8000 Goal/Cnstrnt 2 5000 5400 Goal/Cnstrnt 3 100 0 100 Goal/Cnstrnt 4 50 131.82 Goal/Cnstrot 5 50 531.82 Goal/Cnstrnt 6 0 8072.73 Goal/Cnstrnt 7 100000 0 Goal/Cnstrnt 8 1000 1000 Goal/Cnstrnt 9 500 0 318.18 Goal/Cnstrnt 10 200 381.82 conclusions I can say that the available hours would be used all without downtime between the departments plus the expected profit could be achieved but the prices in the profits of each coat should change since it gives me a positive value outside the target plus the demand of the market could not be adequately satisfied according to the objectives set and the expected