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 1 year 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.
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 ($)
4
6
7
8
Currently, 4,600 pounds of steel and 5,000 machine hours are...
Quiz 4 A manufacturer makes and sales four types of products: Product X, Product Y, Product Z,...
Quiz 4
A manufacturer makes and sales four types of
products: Product X, Product Y, Product Z, and Product
W.
The resources needed to produce one unit of each product and the
sales prices are given in the following Table.
Resource
Product X
Product Y
Product Z
Product W
Steel (lbs)
2
3
4
7
Hours of Machine Time (hours)
3
4
5
6
Sales Price ($)
4
6
7
8
Currently, 4,600 pounds of steel and 5,000 machine hours are...
BC Company sells three products, X, Y, and Z. During October, Product X had sales of...
BC Company sells three products, X, Y, and Z. During October,
Product X had sales of $500,000; Product Y had sales totaling
$300,000; and Product Z reported sales of $200,000. ABC Company
as a whole reported total fixed costs of $443,000, a total
segment margin of $77,000, and a net income of $53,000.
The traceable fixed costs for Product X amounted to $80,000
during October and the traceable fixed costs for Product Z
were $60,000 in October.
Calculate the traceable...
KUMA makes three products X, Y, and Z. All three products must be offered for sale...
KUMA makes three products X, Y, and Z. All three products must
be offered for sale each month in order to provide a complete
market service. The products are fragile and their quality
deteriorates rapidly once they are manufactured.
The products are produced on two types of machine and worked on
by a single grade of direct labour. Five direct employees are paid
Ghc 8 per hour for a guaranteed minimum of 160 hours each per
month.
All of the...
A factory makes a product out of three infinitely- divisible ingredients X, Y , and Z....
A factory makes a product out of three infinitely- divisible
ingredients X, Y , and Z. The ingredients cost p, q, and r pounds
per kg, respectively, with p, q, r > 0 all different, and the
factory has a budget of B > 0 pounds. The value of the product
is some function g(x, y, z)=exp(x+y+z). of the weight of the
ingredients. Solve this problem when the factory wishes to maximize
the value of their product, within their budget.
We are analyzing 2 products – product X and product Y. Product X requires 4 Part...
We are analyzing 2 products – product X and product Y.
Product X requires 4 Part As and 3Part B’s.
Product Y requires 3 Part A’s and 2 Part B’s.
The standard cost for Part A is $24 per unit.
The standard cost for Part B is $12 per unit.
During this month, the company purchased 50,000 units of Part A
for $1,220,000 (there was no beginning balance).
During this month, the company purchased 50,000 units of Part B
for...
QUESTION 1 KUMA makes three products X, Y, and Z. All three products must be offered...
QUESTION 1
KUMA makes three products X, Y, and Z. All three products must
be offered for sale each month in order to provide a complete
market service. The products are fragile and their quality
deteriorates rapidly once they are manufactured.
The products are produced on two types of machine and worked
on by a single grade of direct labour. Five direct employees are
paid Ghc 8 per hour for a guaranteed minimum of 160 hours each per
month.
All...
ABC Company produces Product X, Product Y, and Product Z. All three products require processing on...
ABC Company produces Product X, Product Y, and Product Z. All
three products require processing on specialized finishing
machines. The capacity of these machines is 2,130 hours per month.
ABC Company wants to determine the product mix that should be
achieved to meet the high demand for each product and provide the
maximum profit. Following is information about each product:
Product X Product Y Product Z Selling price $ 149 $ 121 $ 35
Variable costs 104 60 27 Machine...
Find the coordinates of the point (x, y, z) on the plane z = 4 x...
Find the coordinates of the point (x, y, z) on the plane z = 4 x
+ 1 y + 4 which is closest to the origin.
dKristen Company manufactures three products: X, Y, and Z. The demand for each product is 100...
dKristen Company manufactures three products: X, Y, and Z. The
demand for each product is 100 units. The selling price, variable
expenses, and contribution margin for one unit of each product
follow:
Product
X
Y
Z
Selling price
$140
$300
$390
Less variable expenses
(Only Special
steel)
50
100
150
Contribution margin
$90
$200
$240
Steel need to make 1 unit
1 kg
2 kg
3 kg
The same special steel is used for...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Write an HTML file for a web page that contains the items below. Use an internal...
- Individual Brief for group project Members will prepare and share with their team a brief (maximum...
- Find a path that traces the circle in the plane y=0 with radius r=2 and center...
- Imagine that you are a reader of a newspaper that has a section that allows ‘letters...
- Please, i need Unique answer, Use your own words (don't copy and paste). *Please, don't use...
- Python Create a move function that is only defined in the base class called Objects. The...
- Two cars collide at an intersection. Car A, with a mass of 1900 kg , is...
ADVERTISEMENT