Homework1
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School
University of South Florida *
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Course
4312
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
Pages
2
Uploaded by ConstableFish3557
Foundations of Optimization
(ESI 4312) - Fall 202
3
Homework 1
The following questions are present in your textbook Chapter 3 exercise.
Question 1
10 points
The Whitt Window Company, a company with only three employees, makes two different kinds of hand-
crafted windows: a wood-framed and an aluminum-framed window. The company earns $300 profit for
each wood-framed window and $150 profit for each aluminum-framed window. Doug makes the wood
frames and can make 6 per day. Linda makes the aluminum frames and can make 4 per day. Bob forms and
cuts the glass and can make 48 square feet of glass per day. Each wood-framed window uses 6 square feet
of glass and each aluminum-framed window uses 8 square feet of glass. The company wishes to determine
how many windows of each type to produce per day to maximize total profit.
Formulate a linear programming model for this problem.
Question 2
10 points
The WorldLight Company produces two light fixtures (products 1 and 2) that require both metal frame
parts and electrical components. Management wants to determine how many units of each product to
produce so as to maximize profit. For each unit of product 1, 1 unit of frame parts and 2 units of electrical
components are required. For each unit of product 2, 3 units of frame parts and 2 units of electrical
components are required. The company has 200 units of frame parts and 300 units of electrical components.
Each unit of product 1 gives a profit of $1, and each unit of product 2, up to 60 units, gives a profit of $2.
Any excess over 60 units of product 2 brings no profit, so such an excess has been ruled out.
Formulate a linear programming model for this problem.
Question 3
15 points
The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical
centers have placed orders for this month’s production output. The table below shows what the cost would
be for shipping each unit from each factory to each of these customers. Also shown are the number of units
that will be produced at each factory and the number of units ordered by each customer.
A decision now needs to be made about the shipping plan for how many units to ship from each factory to
each customer.
Formulate a linear programming model for this problem.
Question 4
15 points
Larry Edison is the director of the Computer Center for Buckly College. He now needs to schedule the
staffing of the center. It is open from 8 A.M. until midnight. Larry has monitored the usage of the center at
various times of the day, and determined that the following number of computer consultants are required:
Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work
for 8 consecutive hours in any of the following shifts: morning (8 A.M.–4 P.M.), afternoon (noon–8 P.M.),
and evening (4 P.M.–midnight). Full-time consultants are paid $40 per hour.
Part-time consultants can be hired to work any of the four shifts listed in the above table. Part-time
consultants are paid $30 per hour.
An additional requirement is that during every time period, there must be at least 2 full-time consultants on
duty for every parttime consultant on duty.
Larry would like to determine how many full-time and how many part-time workers should work each shift
to meet the above requirements at the minimum possible cost.
Formulate a linear programming model for this problem.
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