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A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $0.80, and each Type B souvenir will result in a profit of $1.80. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 2 hours available on Machine I and 5 hours available on Machine II. (a) For a meaningful solution, the time available on Machine II must lie between 12 X min. (Enter your answers from smallest to largest.) (b) If the time available on Machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for Machine I, then Ace Novelty's profit is maximized by producing 60-k X Type A souvenirs and 240 + k X Type B souvenirs, where -240 ✓ sks 60 X and 96 (c) Find the shadow price for Resource 2 (associated with constraint 2). (Round your answer to the nearest cent.) $216 X

A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $0.80, and each Type B souvenir will result in a profit of $1.80. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 2 hours available on Machine I and 5 hours available on Machine II. (a) For a meaningful solution, the time available on Machine II must lie between 12 X min. (Enter your answers from smallest to largest.) (b) If the time available on Machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for Machine I, then Ace Novelty's profit is maximized by producing 60-k X Type A souvenirs and 240 + k X Type B souvenirs, where -240 ✓ sks 60 X and 96 (c) Find the shadow price for Resource 2 (associated with constraint 2). (Round your answer to the nearest cent.) $216 X

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section4.5: Blending Models
Problem 21P
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A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $0.80, and each Type B souvenir will result in a profit of $1.80. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 2 hours available on Machine I and 5 hours available on Machine II. (a) For a meaningful solution, the time available on Machine II must lie between 12 X and 96 (b) If the time available on Machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for Machine I, then Ace Novelty's profit is maximized by producing 60-k X Type A souvenirs and 240 + k X Type B souvenirs, where -240 ✓ ≤k ≤ 60 X min. (Enter your answers from smallest to largest.) (c) Find the shadow price for Resource 2 (associated with constraint 2). (Round your answer to the nearest cent.) $216 X
Transcribed Image Text:A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $0.80, and each Type B souvenir will result in a profit of $1.80. To manufacture a Type A souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 2 hours available on Machine I and 5 hours available on Machine II. (a) For a meaningful solution, the time available on Machine II must lie between 12 X and 96 (b) If the time available on Machine II is changed from 300 min to (300 + k) min, with no change in the maximum capacity for Machine I, then Ace Novelty's profit is maximized by producing 60-k X Type A souvenirs and 240 + k X Type B souvenirs, where -240 ✓ ≤k ≤ 60 X min. (Enter your answers from smallest to largest.) (c) Find the shadow price for Resource 2 (associated with constraint 2). (Round your answer to the nearest cent.) $216 X
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