Spring 2024 Exam 1 Part 1
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School
Villanova University *
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Course
3008
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
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2
Uploaded by DeaconPelicanMaster997
Spring 2024 Exam 1: Part 1 (50 points)
Instructions:
Please provide final answers in the word document. Many parts of the exam will require the use of Excel. Please create one workbook that contains your work and use tabs to show your work on each part of each problem. You must submit your word doc and Excel file during the time allotted for this exam. There will be a specific submission link for Exam 1 Part 1. Good luck!
1.
D-town brewery brews two beers: Expansion Draft and Burning River. Expansion Draft sells for $18 per barrel, while Burning Rivers sells for $12 per barrel. The unit cost per barrel in both cases found by taking 70% of the sell price. Producing a barrel of Expansion Draft requires 8 pounds of corn and 4 pounds of hops. Producing a barrel of Burning River requires 3 pounds of hops, 2 pounds of corn, and 6 pounds of rice. The brewery has 300 pounds of rice, 500 pounds of corn, and 400 pounds of hops. There is also a requirement that at least 60% of total barrels produced must be Burning River (make sure that you translate this into a linear form. Don’t leave your decision variables in the denominator! Use
algebra to convert to linear form in order to make this compatible with the model we’ve setup). D-town is looking to maximize profit with their production.
a.
Formulate this problem as a linear program in the space below. Note – this should be done in algebraic form (as opposed to how it looks in Excel). (8 points)
b.
Using Excel, solve the linear program. Explain in words how many barrels of each type of
beer D-town should produce and the profit that would come with it. (8 points)
c.
You have an opportunity to purchase 150 additional pounds of rice and/or 150 additional pounds of corn (minimum purchase amounts). The price for rice would be $1 per pound and the price for corn would be $0.50 per pound. What would you advise based on the scenario presented in this problem? Purchase both rice and corn, rice only,
corn only, or neither? Explain and justify your answer. (8 points)
2.
The following tables contains measurements of the key length dimension from a fuel injector. These samples of size five were taken at one-hour intervals. Observations
Sample 1
2
3
4
5
1
0.486
0.499
0.493
0.511
0.481
2
0.499
0.506
0.516
0.476
0.529
3
0.496
0.6
0.515
0.488
0.521
4
0.49
0.506
0.483
0.487
0.489
5
0.47
0.502
0.526
0.469
0.481
6
0.314
0.434
0.467
0.474
0.581
a.
Is this process in control? Please explain based on the results of your control chart (s) and be specific about spread and center in your explanation. The control charts should be pasted into your word document. (14 points) b.
Let’s now assume there is a target key length of 0.495 with a tolerance of 0.09. Is this process capable at a 5 sigma level? If not, be specific about which aspect(s) of the process is/are not capable. If either aspect of the process is inconclusive, indicate it and explain why. (12 points)
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