CED 6030Fall 2022

HOMEWORK 3

You must show your problem-solving process. A solution only cannot get any credits. You are

not allowed to use MS Excel, except for Question 5.

1. Solve the following set of equations.

x – 2y + 3z = 9

-x + 3y = -4

2x – 5y + 5z = 17

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CED 6030

Fall 2022

2. Solve the systems of linear inequalities graphically.

2x + 5y ≤ 20

x – 5y ≥ -5

2

CED 6030

Fall 2022

3. An airline with two types of airplanes, x and y, has contracted with a tour group to

provide accommodation for a minimum of each of 2800 first-class, 2000 tourist, and

5600 economy-class passengers. Airplane x costs $15000 to operate and can

accommodate 40 first-class, 40 tourist, and 20 economy-class passengers, while airplane

y costs $12000 to operate and can accommodate 20 first-class, 10 tourist, and 70

economy-class passengers. If the goal is to find the number of each type to minimize

operating costs, write the objective function and all constraints for this linear

programming problem. Note: You just need to set up LP, so do not solve.

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CED 6030

Fall 2022

4. Solve the linear programming problems by constructing a corner-point table.

Maximize: P = 3x + 2y

subject to:

6x + 3y ≤ 24

3x + 6y ≤ 30

x, y ≥ 0

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CED 6030

Fall 2022

5. Use MS Excel to solve the following question. Attach the screenshot of your Excel sheet

along with your set-up of linear program question.

A fast-food chain plans to expand by opening several new restaurants. The chain operates two

types of restaurants: drive-through and full-service. A drive-through restaurant costs $100,000 to

construct, requires 5 employees, and has an expected annual revenue of $200,000. A full-service

restaurant costs $150,000 to construct, requires 15 employees, and has an expected annual

revenue of $500,000. The chain has $2,400,000 in capital available for expansion. Labor

contracts require that they hire no more than 210 employees, and licensing restrictions require

that they open no more than 20 new restaurants. How many restaurants of each type should the

chain open in order to maximize the expected revenue? What is the maximum expected revenue?

How much of their capital will they use and how many employees will they hire?

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