Applying the Theory of Constraints to Product Mix Decisions
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School
Grant MacEwan University *
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Course
352
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
docx
Pages
3
Uploaded by ritchiem2
1.
Consider a manufacturing company that produces four products: Product A, Product B, Product C,
and Product D.
The total available labor hours for production are limited to 600 hours. The company
has a limited quantity of raw material, which restricts the total production to 1200 units. The total
machine capacity allows for a production output of 1000 units.
The profit per unit for each product is as follows:
Product A generates a profit of $12 per unit.
Product B generates a profit of $10 per unit.
Product C generates a profit of $15 per unit.
Product D generates a profit of $8 per unit.
Formulate the optimal product mix problem as a linear program. Solve it using excel. It is ok if your
answers are in decimals.
2. A company makes four products that have the following characteristics: Product A sells for $70 but
needs $20 of materials and $15 of labor to produce; Product B sells for $55 but needs $25 of materials and
$10 of labor to produce; Product C sells for $80 but needs $35 of materials and $15 of labor to produce;
Product D sells for $75 but needs $35 of materials and $15 of labor to produce. The processing
requirements for each product on each of the four machines are shown in the table.
Processing Time (min/unit)
Work Center
A
B
C
D
W
5
3
7
5
X
7
6
6
4
Y
10
5
5
8
Z
6
6
5
3
Work centers W, X, Y, and Z are available for 40 hours per week and have no setup time when switching
between products. Market demand for each product is 100 units per week. In the questions that follow, the
traditional method
refers to maximizing the contribution margin per unit for each product, and the
bottleneck method
refers to maximizing the contribution margin per minute at the bottleneck for each
product.
3. Given the following information about a project, answer the questions:
Path
Expected
durations
Varianc
e
A
29
4
B
31
9
C
28
1
a)
What is the probability that the project will be finished between 30 and 32 days?
b)
Given that a delay in the project beyond 31 days incurs a penalty of $50,000, what is the
expected penalty?
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