Question
In: Advanced Math
Quiz 4 A manufacturer makes and sales four types of products: Product X, Product Y, Product Z,...
Quiz 4
A manufacturer makes and sales four types of products: Product X, Product Y, Product Z, and Product W.
The resources needed to produce one unit of each product and the sales prices are given in the following Table.
|
Resource |
Product X |
Product Y |
Product Z |
Product W |
|
Steel (lbs) |
2 |
3 |
4 |
7 |
|
Hours of Machine Time (hours) |
3 |
4 |
5 |
6 |
|
Sales Price ($) |
4 |
6 |
7 |
8 |
- Currently, 4,600 pounds of steel and 5,000 machine hours are available.
- To meet customer demands, exactly 950 total products must be produced.
- Customers also demand that at least 400 units of Product W be produced.
Formulate an LP that can be used to maximize sales revenue for the manufacturer.
LP Formula
Let Pi be the number of product type i produced by the manufacturer, where i = X, Y, X, and W.
MAXIMIZE 4 PX + 6 PY + 7 PZ + 8 PW
Subject To
2 PX + 3 PY + 4 PZ + 7 PW <= 4600 ! Available Steel
3 PX + 4 PY + 5 PZ + 6 PW <= 5000 ! Available Machine Hours
PX + PY + PZ + PW = 950 ! Total Demand
PW >= 400 ! Product W Demand
PX >=0
PY >=0
PZ >=0
PW >=0
Suppose that 4,500 pounds of steel are available. What is the new optimal z-value?
|
Objective Function Value: |
|
|
PX: |
|
|
PY: |
|
|
PZ: |
|
|
PW: |
What if only 4,400 pounds of steel are available? What is the new optimal z-value?
|
Objective Function Value: |
|
|
PX: |
|
|
PY: |
|
|
PZ: |
|
|
PW: |
What is the most that manufacturer should be willing to pay for an additional unit of raw material?
What is the most that manufacturer should be willing to pay for an additional unit of machine hour?
In order to answer the above questions, how many times you did update your model and solve it?
Solutions
Expert Solution
A) Quantity of Steel = 4600
| Resource | Product X | Product Y | Product Z | Product W | |
| Pi | 50 | 450 | 0 | 450 | 950 |
| Steel (lbs) | 2 | 3 | 4 | 7 | 4600 |
| Hours of Machine Time (hours) | 3 | 4 | 5 | 6 | 4650 |
| Sales Price ($) | 4 | 6 | 7 | 8 | 6500 |
B) Quantity of Steel = 4500
| Resource | Product X | Product Y | Product Z | Product W | |
| Pi | 150 | 350 | 0 | 450 | 950 |
| Steel (lbs) | 2 | 3 | 4 | 7 | 4500 |
| Hours of Machine Time (hours) | 3 | 4 | 5 | 6 | 4550 |
| Sales Price ($) | 4 | 6 | 7 | 8 | 6300 |
C) Quantity of Steel = 4400
| Resource | Product X | Product Y | Product Z | Product W | |
| Pi | 250 | 250 | 0 | 450 | 950 |
| Steel (lbs) | 2 | 3 | 4 | 7 | 4400 |
| Hours of Machine Time (hours) | 3 | 4 | 5 | 6 | 4450 |
| Sales Price ($) | 4 | 6 | 7 | 8 | 6100 |
Colby Messinger answered 2 years agoRelated Solutions
Quiz 4 A manufacturer makes and sales four types of products: Product X, Product Y, Product Z,...
Quiz 4
A manufacturer makes and sales four types of
products: Product X, Product Y, Product Z, and Product
W.
The resources needed to produce one unit of each product and the
sales prices are given in the following Table.
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Product X
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Steel (lbs)
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Sales Price ($)
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Currently, 4,600 pounds of steel and 5,000 machine hours are...
Quiz 4 A manufacturer makes and sales four types of products: Product X, Product Y, Product Z,...
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A manufacturer makes and sales four types of
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The resources needed to produce one unit of each product and the
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Product X
Product Y
Product Z
Product W
Steel (lbs)
2
3
4
7
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3
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5
6
Sales Price ($)
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