Special D, Inc., is a new firm that is engaged in recycling. Its main facility uses a three- step system to process beverage containers. A consultant has developed the following LP model of the process: maximize Z = 14Q + 1IR + 157 (revenue) subject to Sorting Crushing Packing 2.4Q + 3.0R + 4.07 < 960 minutes 2.5Q + 1.8R + 2.4T < 607 minutes 12Q + 18R + 24T < 3,600 minutes Q, R, and T> O The consultant has also included an Excel output of sensitivity analysis, shown Answer these questions using the information: Which decision variables are in the final solution? What are their optimal values? a. b. Finthe range of optimality for the variables that are in the final solution. Find the range of insignificance for R. d. Identify the shadow price for each constraint. Determine the range over which each shadow price is valid. By how much would revenue decrease if sorting time was reduced to 900 minutes? How much would revenue increase if С. e. f. rting time was increased to 1,269 minutes? What effect would an increase of $2 in the revenue per unit of Thave on the opti- g. mal value of T? On the total revenue? h. Would an increase of $1 in the revenue per unit of Rhave any impact on the opti- mal solution? Explain. i. If you could obtain additional quantities of one resource (either sorting, crushing, or packing) at no additional cost, and your goal was to achieve the greatest increase in revenue, which resource would you add, and how much of it would you add? Explain.
Special D, Inc., is a new firm that is engaged in recycling. Its main facility uses a three- step system to process beverage containers. A consultant has developed the following LP model of the process: maximize Z = 14Q + 1IR + 157 (revenue) subject to Sorting Crushing Packing 2.4Q + 3.0R + 4.07 < 960 minutes 2.5Q + 1.8R + 2.4T < 607 minutes 12Q + 18R + 24T < 3,600 minutes Q, R, and T> O The consultant has also included an Excel output of sensitivity analysis, shown Answer these questions using the information: Which decision variables are in the final solution? What are their optimal values? a. b. Finthe range of optimality for the variables that are in the final solution. Find the range of insignificance for R. d. Identify the shadow price for each constraint. Determine the range over which each shadow price is valid. By how much would revenue decrease if sorting time was reduced to 900 minutes? How much would revenue increase if С. e. f. rting time was increased to 1,269 minutes? What effect would an increase of $2 in the revenue per unit of Thave on the opti- g. mal value of T? On the total revenue? h. Would an increase of $1 in the revenue per unit of Rhave any impact on the opti- mal solution? Explain. i. If you could obtain additional quantities of one resource (either sorting, crushing, or packing) at no additional cost, and your goal was to achieve the greatest increase in revenue, which resource would you add, and how much of it would you add? Explain.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section4.8: Data Envelopment Analysis (dea)
Problem 42P
Related questions
Question
Please solve for parts f, g , h & i.
Transcribed Image Text:Special D, Inc., is a new firm that is engaged in recycling. Its main facility uses a three-
step system to process beverage containers. A consultant has developed the following
LP model of the process:
maximize
Z = 14Q + 1IR + 157
(revenue)
subject to
Sorting
Crushing
Packing
2.4Q + 3.0R + 4.07 < 960 minutes
2.5Q + 1.8R + 2.4T < 607 minutes
12Q + 18R + 24T < 3,600 minutes
Q, R, and T> O
The consultant has also included an Excel output of sensitivity analysis, shown
Answer these questions using the information:
Which decision variables are in the final solution? What are their optimal values?
a.
b.
Finthe
range
of optimality for the variables that are in the final solution.
Find the range of insignificance for R.
d. Identify the shadow price for each constraint.
Determine the range over which each shadow price is valid.
By how much would revenue decrease if sorting time was reduced to 900 minutes?
How much would revenue increase if
С.
e.
f.
rting time was increased to 1,269 minutes?
What effect would an increase of $2 in the revenue per unit of Thave on the opti-
g.
mal value of T? On the total revenue?
h. Would an increase of $1 in the revenue per unit of Rhave any impact on the opti-
mal solution? Explain.
i.
If you could obtain additional quantities of one resource (either sorting, crushing, or
packing) at no additional cost, and your goal was to achieve the greatest increase in
revenue, which resource would you add, and how much of it would you add? Explain.
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