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You work for the Brad's Nailer Company which manufactures two types of nailers: a pneumatic model and a cordless model. You have contracted to supply a national retail chain with both pneumatic nailers and cordless nailers; the minimum number of nailers is given below. However, Brad's nailer production capability is limited in three departments: production, testing, and packaging. To minimize your costs, you have determined to ship more cordless nailers than pneumatic. (The number of nailers must be a whole number.) Your answer will be the production hours needed to execute your production plan - rounded to the nearest whole hour. Use Scenario 3 Pneum. Cost Pneum. Prod Hrs Pneum. Test Hrs Pneum. Pkg Hrs Pneum. Sales Cordless Cost Cordless Prod Hrs Cordless Test Hrs Cordless Pkg Hrs Cordless Sales Prod Hrs max Testing Hrs max Pkg Hrs max Scenario 1 52 0.2 0.3 0.1 22,000 47 0.3 0.4 0.1 15,500 13,000 17,000 4,500 Scenario 2 Scenario 3 Scenario 4 55.50 0.4 0.3 0.1 24,500 69.75 0.3 0.5 0.1 15,500 20,000 21,000 5,500 38.50 0.25 0.4 0.1 18,000 34 0.4 0.4 0.2 14,000 21,500 18,000 5,500 79 .4 .25 .15 7,500 52 .4 .3 .1 5,000 20,000 17,000 5,500

You work for the Brad's Nailer Company which manufactures two types of nailers: a pneumatic model and a cordless model. You have contracted to supply a national retail chain with both pneumatic nailers and cordless nailers; the minimum number of nailers is given below. However, Brad's nailer production capability is limited in three departments: production, testing, and packaging. To minimize your costs, you have determined to ship more cordless nailers than pneumatic. (The number of nailers must be a whole number.) Your answer will be the production hours needed to execute your production plan - rounded to the nearest whole hour. Use Scenario 3 Pneum. Cost Pneum. Prod Hrs Pneum. Test Hrs Pneum. Pkg Hrs Pneum. Sales Cordless Cost Cordless Prod Hrs Cordless Test Hrs Cordless Pkg Hrs Cordless Sales Prod Hrs max Testing Hrs max Pkg Hrs max Scenario 1 52 0.2 0.3 0.1 22,000 47 0.3 0.4 0.1 15,500 13,000 17,000 4,500 Scenario 2 Scenario 3 Scenario 4 55.50 0.4 0.3 0.1 24,500 69.75 0.3 0.5 0.1 15,500 20,000 21,000 5,500 38.50 0.25 0.4 0.1 18,000 34 0.4 0.4 0.2 14,000 21,500 18,000 5,500 79 .4 .25 .15 7,500 52 .4 .3 .1 5,000 20,000 17,000 5,500

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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You work for the Brad's Nailer Company which manufactures two types of nailers: a pneumatic model and a cordless model. You have contracted to supply a national retail chain with both pneumatic nailers and cordless nailers; the minimum number of nailers is given below. However, Brad's nailer production capability is limited in three departments: production, testing, and packaging. To minimize your costs, you have determined to ship more cordless nailers than pneumatic. (The number of nailers must be a whole number.) Your answer will be the production hours needed to execute your production plan - rounded to the nearest whole hour. Use Scenario 3 Pneum. Cost Pneum. Prod Hrs Pneum. Test Hrs Pneum. Pkg Hrs Pneum. Sales Cordless Cost Cordless Prod Hrs Cordless Test Hrs Cordless Pkg Hrs Cordless Sales Prod Hrs max Testing Hrs max Pkg Hrs max Scenario 1 52 0.2 0.3 0.1 22,000 47 0.3 0.4 0.1 15,500 13,000 17,000 4,500 Scenario 2 Scenario 3 Scenario 4 55.50 0.4 0.3 0.1 24,500 69.75 0.3 0.5 0.1 15,500 20,000 21,000 5,500 38.50 0.25 0.4 0.1 18,000 34 0.4 0.4 0.2 14,000 21,500 18,000 5,500 79 .4 .25 .15 7,500 52 .4 .3 .1 5,000 20,000 17,000 5,500
Transcribed Image Text:You work for the Brad's Nailer Company which manufactures two types of nailers: a pneumatic model and a cordless model. You have contracted to supply a national retail chain with both pneumatic nailers and cordless nailers; the minimum number of nailers is given below. However, Brad's nailer production capability is limited in three departments: production, testing, and packaging. To minimize your costs, you have determined to ship more cordless nailers than pneumatic. (The number of nailers must be a whole number.) Your answer will be the production hours needed to execute your production plan - rounded to the nearest whole hour. Use Scenario 3 Pneum. Cost Pneum. Prod Hrs Pneum. Test Hrs Pneum. Pkg Hrs Pneum. Sales Cordless Cost Cordless Prod Hrs Cordless Test Hrs Cordless Pkg Hrs Cordless Sales Prod Hrs max Testing Hrs max Pkg Hrs max Scenario 1 52 0.2 0.3 0.1 22,000 47 0.3 0.4 0.1 15,500 13,000 17,000 4,500 Scenario 2 Scenario 3 Scenario 4 55.50 0.4 0.3 0.1 24,500 69.75 0.3 0.5 0.1 15,500 20,000 21,000 5,500 38.50 0.25 0.4 0.1 18,000 34 0.4 0.4 0.2 14,000 21,500 18,000 5,500 79 .4 .25 .15 7,500 52 .4 .3 .1 5,000 20,000 17,000 5,500
Expert Solution
Step 1

Let 'P' be pneumatic nailers to be produced,

and let 'C' be the cordless nailers to be produced.

Min Z = 38.5P + 34C

The constraints developed as per scenario 3 are:

 

1. Production hours 0.25P +0.40C ≤21500

2. Testing hours 0.40P +0.40C ≤18000

3. Packaging hours 0.1P +0.2C ≤5500

4. P ≥18000

5. C ≥14000

 

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