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[solution]: QMB3600 HW-9 Problem #1 A refrigerator manufacturer makes 3

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QMB3600 HW-9

Problem #1

A refrigerator manufacturer makes 3 models: Mini, Standard, and Large. Upon selling these

products, the profit realized per unit is:

Mini:

$150

Standard: $200

Large:

$250

In order to produce each model, the parts? requirements are as follows:

Number of

Grill covers

Mini

Standard

Large

Number of

Ice Makers

1

1

2

1

2

2

Manufacturing

Time (hours)

6

10

15

During the next manufacturing cycle, the inventory department has 600 Grill Covers and 800

Ice Makers in stock. The factory has 3000 hours of manufacturing time available.

We would like to determine how many Mini models (M), Standard models (S), and Large

models (L) should the company make to maximize profit.

The linear programming model for the problem is:

Max (150M + 200S + 250L)

s.t. 1M + 1S + 2L

<

1M + 2S + 2L <

6M + 10S + 15L <

M, S, L > 0

600

800

3000

Grill Covers

Ice Makers

Manufacturing Time

Questions:

1. Determine the solution to the above problem using MS Excel ? use the approach

described in the handout posted earlier on Blackboard. Print and submit your solution

from the MS Excel spreadsheet.

2. On the printout of the solution, clearly explaining the reason for your answers, identify

the following:

a. the optimal solution, i.e. decision variable values.

b. maximum value of the objective function.

c. binding constraints.

d. non-binding constraints.

e. For resources that are not fully utilized, how much is unutilized?

Problem #2

Solve the following Linear Programming problem graphically (to scale) and identify the

optimal solution and the corresponding value of the objective function. USE GRAPH PAPER

utilizing the entire sheet. If you do not use graph paper no credit will be given.

Max (18x1 + 12x2)

s.t.

2x1 + x2

<

x2

>

x1 + x2

=

x1 , x2 > 0

40

10

40

1. Where is the feasible region?

2. What is the optimal solution?

3. What is the maximum value of the objective function?

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STATUSAnswered

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DATE ANSWEREDDec 18, 2020

EXPERTTutor

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