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
1
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.
3
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
4
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?
5
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