Exam 2

docx

School

Northwest Mississippi Community College *

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Course

530

Subject

Business

Date

Apr 3, 2024

Type

docx

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Uploaded by zzylla15

SCMS 3711: Exam 2 Assigned: April 6, 2023, at 9:40 am/1:00 pm Due: Electronically via Canvas by April 6 by 11:05 am/2:25 pm. Total Duration: 1hr 25 mins Please sign the below: 1. I did not receive any external help during the Final Exam. 2. I did not provide any help to my classmates during the Final Exam. 3. I will not disclose the exam to anyone. ____________________________ Signature Rules for submitting Exam 2: 1. Please work individually. 2. No search in internet is allowed. 3. Your Exam submission should contain at least one Excel file (Use different tabs for different questions and name them appropriately ) 4. Please save your files in the following format: Exam2_First Name _First Letter of your last name (example: If I were to submit my exam, I would name the file as Exam2_Punya_C.) 1

Part 1: Conceptual Questions (2 points) [Please select all correct options] Q1. Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem? (1 point) a. 2 X 1 + √ X 2 ≥ 60 b. 3 X 1 + 2 X 2 − 3 X 3 X 1 + X 2 + X 3 ≤ 0.9 c. X 1 ≥ X 2 Ans: Q2. Which of the following constraints can make an objective function Max x + y unbounded? (1 point) a. x≤ 0 , y≤ 0 b. x≥ 0 , y ≤ 0 c. x≤ 0 , y≥ 0 Ans: Part 2: Modelling Questions (8 points) Q3. Fordco Problem (3 points): Fordco produces cars in Detroit and Dallas. The Detroit plant can produce up to 6500 cars and Dallas plant can produce up to 6000 cars. Cars must be shipped to three cities. City 1 must receive 5000 cars, City 2 must receive 4000 cars, and City 3 must receive 3000 cars. The costs of shipping a car from each plant to each city are given below: 2

City 1 City 2 City 3 Detroit $800 $600 $300 Dallas $500 $200 $200 a. Create a model in Excel and determine how many cars to ship from each plant to each city in order to minimize the total cost of meeting all demands. (1 point) b. What are the binding and unbinding constraints in your model? (0.5 points) Ans: c. What happens to your solution if shipping from Detroit to City 1 is not allowed? (0.5 points) Ans: d. If you could generate an extra unit of demand at one of the cities, which one would you choose? Why? (1 point) Ans: Q4. Knapsack Problem: (3 Points) The name "knapsack problem" dates back to the early works of mathematician Tobias Dantzig (1884– 1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage. The picture below summarizes the problem: which boxes should be chosen to maximize the amount of money while keeping the overall weight under or equal to 15 kg? Assume that only one of each box is available and you can only either take the whole of a box or nothing at all. 3

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a. Solve the Knapsack problem in Solver and tell me your strategy below. (1 point) (You can name the boxes using their colors: green, gray, orange, yellow, and blue.) b. What happens to your solution when you want to include the yellow box for sure. (1 point) c. What happens to your solution when you do not want to include the blue box. (1 point) Q5. Craft Jewelry Business (2 points) A woman makes craft jewelry to sell at a seasonal craft show. She makes pins and earrings. Each pin takes her 1 hour to make and sells for a profit of $8. The pairs of earrings take 2 hours to make, but she gets a profit of $20. She likes to have variety, so she wants to have at least as many pins as pairs of earrings. She knows that she has approximately 40 hours for creating jewelry between now and the start of the show. She also knows that the craft show vender wants sellers to have more than 20 items on display at the beginning of the show. Assuming she sells all her inventory, how many each of pins and earring pairs should the woman make to maximize her profit? 4

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