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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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