Question

A manufacturing firm has discontinued the production of a certain unprofitable product line. Considerable excess production capacity was created as a result. Management is considering devoting this excess capacity to one or more of three products: X1, X2, and X3. Machine hours required per unit are: PRODUCT MACHINE TYPE X1 X2 X3Milling machine 8 2 3Lathe 4 3 0Grinder 2 0 1The available time in machine hours per week isMACHINE HOURS PER WEEKMilling machines 800Lathes 480Grinders 320The salespeople estimate they can sell all the units of X1 and X2 that can be made, But the sales potential of X3 is 80 units per week maximum.Unit profits for the three products are $20 (for X1), $6 (for X2), and $8 (for X3).Required:(a) Write the mathematical formulation to maximize the profit per week (Decision variables: Production amount of X1, X2, and X3).(b) Solve the mathematical formulation using Excel Solver. Show your work.(c) What is the optimal solution?

Answer 1

Answer:

Please kindly check explaination for the details.

Explanation:

a.

Decision variables:

Let

X1 = no of units of product X1

X2 = no of units of product X2

X3 = no of units of product X3

Objective function is to maximize profits

Max Z = 20X1 + 6X2 + 8X3

Constraints:

8X1 + 2X2 + 3X3 <= 800

4X1 + 3X2 <= 480

2X1 + X3 <= 320

X1, X2, X3>=0

b.

please see attachment for the excel solutions.

c.

X1 = 0

X2 = 160

X3 = 160

Z = 2240