Question

Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:Department Product 1 Product 2 Product 3A 1.50 3.00 2.00B 2.00 1.00 2.50C 0.25 0.25 0.25During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3.Formulate a linear programming model for maximizing total profit contribution. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)Let Pi = units of product i produced

Answer 1

Missing Part of the Question

The management also stated that we should not consider making more than 175 units for product 1, 150units of product 2, or 140 units of product 3.

Answer and Explanation:

Given

Department ----- Product 1 -----Product 2 ------ Product 3

A ---------- 1.50 ------- 3.00 -------- 2.00

B --------- 2.00 ------- 1.00 -------- 2.50

C --------- 0.25 --------- 0.25 -------- 0.25

The profit contributions per unit are

Product 1 = $25

Product 2 = $28

product 3 = $30

The set up costs are

Product 1 = $400

Product 2 = $550

Product 3 =$600

The labor-hours available are

Department A = 450

Department B = 350

Department C = 50

Formulating a linear programming model, as have

Let X be the number of units produced

Max Z = 25X1 + 28X2 + 30X3 - 400Y1 - 550Y2 - 600Y3

Subjected to (the constraints are)

1.5X1 + 3X2 + 2X3 ≤ 450

2X1 + X2 + 2.5X3 ≤ 350

0.25X1 + 0.25X2 + 0.25X3 ≤ 50

0 ≤ X1 ≤ 175Y1

0 ≤ X2 ≤ 150Y2

0 ≤ X3 ≤ 140Y3

The first three constraints represents the labour hours in departments A, B and C.

While the last three constraints represents the maximum production of product 1,2 and 3.

Answer 2

       Formulate a linear programming model for maximizing total profit        contribution:

Given data :

Department ----- Product 1 -----Product 2 ------ Product 3

               A               1.50               3.00                   2.00

                B               2.00               1.00                   2.50

               C               0.25                  0.25                0.25

The profit contributions per unit are :

• Product 1 = $25

• Product 2 = $28

• Product 3 = $30

The set up costs are:

• Product 1 = $400
• Product 2 = $550
• Product 3 =$600

The labor-hours available are

• Department A = 450
• Department B = 350
• Department C = 50

Formulating a linear programming model, as have

Let A be the number of units produced

Max  C = 25A1 + 28A2 + 30A3 - 400B1 - 550B2 - 600B3

• 5A1 + 3A2 + 2A3 ≤ 450
• 2A1 + A2 + 2.5A3 ≤ 350
• 0.25A1 + 0.25A2 + 0.25A3 ≤ 50
• 0 ≤ A1 ≤ 175B1
• 0 ≤ A2 ≤ 150B2
• 0 ≤ A3 ≤ 140B3

 

A linear programming model for maximizing total profit contribution are the last three constraints of Product 1,product 2 and product 3.

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