A manufacturing plant is producing the following products using available raw materials shown in the below Table. Resource d) e) follow: Raw material 1 Raw material 2 Unit profit Resource usage per unit product Product 2 3 1 2 Product 1 1 1 1 Available resource 8 4 Company aims to determine the optimal number of products to be produced in order to maximize the total profit. a) Formulate the problem using algebraic method. b) Solve the model using the graphical method (indicate optimal solution and profit). c) Use graphical method to determine the shadow price for each of these resources (based on the definition of shadow price and by increasing each resource by one unit and solving the problem again). Use the Excel solver to do parts b and c. Using Solver Table generate the optimal solution and the total profit for each resource as e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1) e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1) e3: Consider simultaneous changes for both unit profits in part e1 and e2 using given ranges. e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1) e5: Consider available resource of Raw material 2 (use range from 2 to 10 and increment of 1) e6: Consider simultaneous changes for both resources in part e4 and e5 using given ranges. f) Using Excel Solver generate a sensitivity report. Determine allowable ranges for coefficients of objective function and Right-hand side resources. Explain what they mean. Find the shadow price for each resource, explain their meaning and advantages/flexibilities they can provide for management.
A manufacturing plant is producing the following products using available raw materials shown in the below Table. Resource d) e) follow: Raw material 1 Raw material 2 Unit profit Resource usage per unit product Product 2 3 1 2 Product 1 1 1 1 Available resource 8 4 Company aims to determine the optimal number of products to be produced in order to maximize the total profit. a) Formulate the problem using algebraic method. b) Solve the model using the graphical method (indicate optimal solution and profit). c) Use graphical method to determine the shadow price for each of these resources (based on the definition of shadow price and by increasing each resource by one unit and solving the problem again). Use the Excel solver to do parts b and c. Using Solver Table generate the optimal solution and the total profit for each resource as e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1) e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1) e3: Consider simultaneous changes for both unit profits in part e1 and e2 using given ranges. e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1) e5: Consider available resource of Raw material 2 (use range from 2 to 10 and increment of 1) e6: Consider simultaneous changes for both resources in part e4 and e5 using given ranges. f) Using Excel Solver generate a sensitivity report. Determine allowable ranges for coefficients of objective function and Right-hand side resources. Explain what they mean. Find the shadow price for each resource, explain their meaning and advantages/flexibilities they can provide for management.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.5: Shortest Path Models
Problem 30P
Related questions
Question
Company aims to determine the optimal number of products to be produced in order to maximize the total profit.
a)
Formulate the problem using algebraic method.
b) Solve the model using the graphical method (indicate optimal solution and profit).
C)
again).
Use graphical method to determine the shadow price for each of these resources (based on the definition of shadow price and by increasing each resource by one unit and solving the problem
d)
Use the Excel solver to do parts b and c.
e)
follow:
Using Solver Table generate the optimal solution and the total profit for each resource as
e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1)
e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1)
е3: Consider simultaneous changes for both unit profits in part e1 and e2 using given ranges.
e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1)
e5: Consider available resource of Raw material 2 (use range from 2 to 10 and increment of 1)
e6: Consider simultaneous changes for both resources in part e4 and e5 using given ranges.
f)
Using Excel Solver generate a sensitivity report. Determine allowable ranges for coefficients of objective function and Right-hand side resources. Explain what they mean. Find the shadow price for each resource, explain their meaning and advantages/flexibilities they can provide for management.
Transcribed Image Text:Question 1:
A manufacturing plant is producing the following products using available raw materials shown in
the below Table.
Resource
Raw material 1
Raw material 2
Unit profit
d)
e)
follow:
Resource usage per unit product
Product 2
3
1
2
Product 1
1
1
1
Available resource
8
4
Company aims to determine the optimal number of products to be produced in order to maximize
the total profit.
a)
Formulate the problem using algebraic method.
b)
Solve the model using the graphical method (indicate optimal solution and profit).
c)
Use graphical method to determine the shadow price for each of these resources (based on
the definition of shadow price and by increasing each resource by one unit and solving the problem
again).
Use the Excel solver to do parts b and c.
Using Solver Table generate the optimal solution and the total profit for each resource as
e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1)
e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1)
e3: Consider simultaneous changes for both unit profits in part el and e2 using given ranges.
e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1)
e5: Consider available resource of Raw material 2 (use range from 2 to 10 and increment of 1)
e6: Consider simultaneous changes for both resources in part e4 and e5 using given ranges.
f)
Using Excel Solver generate a sensitivity report. Determine allowable ranges for coefficients
of objective function and Right-hand side resources. Explain what they mean. Find the shadow price
for each resource, explain their meaning and advantages/flexibilities they can provide for
management.
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Step 1: Examine - Given details:
VIEWStep 2: a) Examine - Objective Functions and Constraints:
VIEWSolution
VIEWStep 3: b) Calculate - Optimal Solutions and Profit:
VIEWStep 4: c) Calculate - Shadow price:
VIEWStep 5: d) Calculate - Optimal Solutions and Profit:
VIEWStep 6: e1) Calculate - Unit profit for Product 1:
VIEWStep 7: e2) Calculate - Unit profit for Product 2:
VIEWStep 8: e3) Calculate - Unit profit for both product:
VIEWStep 9: e4) Calculate - Unit profit for Raw Material 1:
VIEWStep 10: Calculate - Part e5, e6 and f:
VIEW
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