The objective is to minimize shipping costs C = Subjects to the contraints Priva
ID: 467597 • Letter: T
Question
The objective is to minimize shipping costs C = Subjects to the contraints
Private Motors, Inc., has two plants, M1 and M2, which manufacture engines; the company also has two assembly plants, A1 and A2, which assemble the cars. M1 can produce at most 600 engines per week. M2 can produce at most 400 engines per week. A1 needs at least 500 engines per week and A2 needs at least 200 engines per week. Following is a table of charges to ship engines to assembly plants Al A2 M1 $400 $100 M2 $200$300 How many engines should be shipped each week from each engine plant to each assembly plant? [Hint: Consider four variables: of units shipped from M1 to A1, of units shipped from M1 to A2, of units shipped from M2 to A1, and of units shipped from M2 to A2.] a) Formulate a linear programming problem that models the problem. Let denote the total shipping cost, x2 = the number of units shipped from M1 to A2, X3 the number of units shipped from 2 to AI, and X4 (b) Solve the linear programming problem. the number of units shipped from M1 to A the number of units shipped from M2 to A2. (c) Analyze the solution.Explanation / Answer
x1 = 100
x2 = 200
x3 = 400
x4 = 0
c.1).To ship the above mentioned quantity, the min. total cost = $ 240000 and not $ 210000
c.2) To ship the above mentioned quantity, the min. total cost = $ 230000 and not $ 210000
c.3) To ship the above mentioned quantity, the min. total cost = $ 150300 and not $ 150000
c.4) To ship the above mentioned quantity, the min. total cost = $ 140000 and with in $ 150000
A1 A2 M1 400 100 600 M2 200 300 400 500 200 Dec. Var. A1 A2 M1 x1 x2 M2 x3 x4 Changing Cells Dec. Var. A1 A2 M1 100 200 M2 400 0 Constraints RHS LHS x1+x2 300 <= 600 x3+x4 400 <= 400 x1+x3 500 >= 500 x2+x4 200 >= 200 x1,x2,x3,x4 >= 0 Obj.Function = 140000