A D Wine Beer Champagne Whiskey Molding time 4 min. 9 min. 7 min. 10 min. Packaging time 1 min. 1 min. 3 kg $6 3 min. 40 min. 4 kg $10 2 kg $9 20 kg $20 Raw material Selling price Glass Co. manufactures drink glasses: wine, beer, champagne, and whiskey. Each type of glass requires time in the molding shop, time in the packaging shop, and raw material, as given in the table below. Currently, 600 minutes of molding time, 400 minutes of packaging time, and 500 kg of raw material are available. Assuming that Glass Co. wants to maximize revenue, the following LP should be solved; Мaximize Z- 6x1 +10х2+ 9х3 + 20х4, subject to 4x1 + 9x2 + 7x3 + 10x4< 600 (Molding constraint) x1 + x2 + 3x3 + 40x4< 400 (Packaging constraint) 3x1 + 4x2 + 2x3 + 20x4< 500 (Raw material constraint) х1, х2, хз, х4 > 0. For each of the following parts, answer the question specifically and completely. Each part is independent (that is, any change made to the model in one part does not apply to any other parts). 1) Suppose the price per a whiskey glass changes to $16. What will be the new optimal revenue? 2) Suppose the company discovers that 20 kg of raw material is destroyed and cannot be used anymore. What will be the new optimal revenue? 3) Suppose the price for a champagne glass changes to $9.1. Will the company produce champagne glass in this case? Explain why.
A D Wine Beer Champagne Whiskey Molding time 4 min. 9 min. 7 min. 10 min. Packaging time 1 min. 1 min. 3 kg $6 3 min. 40 min. 4 kg $10 2 kg $9 20 kg $20 Raw material Selling price Glass Co. manufactures drink glasses: wine, beer, champagne, and whiskey. Each type of glass requires time in the molding shop, time in the packaging shop, and raw material, as given in the table below. Currently, 600 minutes of molding time, 400 minutes of packaging time, and 500 kg of raw material are available. Assuming that Glass Co. wants to maximize revenue, the following LP should be solved; Мaximize Z- 6x1 +10х2+ 9х3 + 20х4, subject to 4x1 + 9x2 + 7x3 + 10x4< 600 (Molding constraint) x1 + x2 + 3x3 + 40x4< 400 (Packaging constraint) 3x1 + 4x2 + 2x3 + 20x4< 500 (Raw material constraint) х1, х2, хз, х4 > 0. For each of the following parts, answer the question specifically and completely. Each part is independent (that is, any change made to the model in one part does not apply to any other parts). 1) Suppose the price per a whiskey glass changes to $16. What will be the new optimal revenue? 2) Suppose the company discovers that 20 kg of raw material is destroyed and cannot be used anymore. What will be the new optimal revenue? 3) Suppose the price for a champagne glass changes to $9.1. Will the company produce champagne glass in this case? Explain why.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you solve this question?
Transcribed Image Text:Glass
A
В
D
Wine
Beer Champagne Whiskey
7 min.
Molding time
4 min. 9 min.
10 min.
Packaging time 1 min. 1 min.
3 kg 4 kg
$10
3 min.
40 min.
Raw material
2 kg
20 kg
$20
Selling price
$6
$9
Glass Co. manufactures drink glasses: wine, beer, champagne, and whiskey.
Each type of glass requires time in the molding shop, time in the packaging
shop, and raw material, as given in the table below.
Currently, 600 minutes of molding time, 400 minutes of packaging time, and 500 kg
of raw material are available. Assuming that Glass Co. wants to maximize revenue,
the following LP should be solved;
Мaximize Z- 6x1 + 10х2+ 9х3 + 20х4,
subject to
4x1 + 9x2 + 7x3 + 10x4< 600 (Molding constraint)
x1 + x2 + 3x3 + 40x4 < 400 (Packaging constraint)
3x1 + 4x2 + 2x3 + 20x4< 500 (Raw material constraint)
х1, х2, х3, х4 2 о.
For each of the following parts, answer the question specifically and completely.
Each part is independent (that is, any change made to the model in one part does
not apply to any other parts).
1) Suppose the price per a whiskey glass changes to $16. What will be the new
optimal revenue?
2) Suppose the company discovers that 20 kg of raw material is destroyed and
cannot be used anymore. What will be the new optimal revenue?
3) Suppose the price for a champagne glass changes to $9.1. Will the company
produce champagne glass in this case? Explain why.
Objective value: 920.0000
Variable
Value
Reduced Cost
0.000000
A
140.0000
B
0.000000
0.000000
4.000000
2.400000
0.200000
0.000000
D
Row
Slack or Surplus
0.000000
100.0000
Dual Price
1.2000po
0.000000
2
3
0.000000
0.400000
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