Assignment 6(1)
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University of Texas, Dallas *
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Course
3333
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
4
Uploaded by AdmiralMule126
Assignment 6
1
Question 1.
(30 points) You are provided with the following
integer program
.
min
z
= 3
x
−
y
s.t.
x
+
y
≤
10
x
−
y
≥
1
.
5
x
+ 3
y
≥
5
x
≤
9
.
5
y
≤
3
.
5
x, y
≥
0
and integer
(a) On the following page, use the graphical solution method to identify the
feasible
points
.
(Use the scale 1 by 1 for each small square so that you can visually
detect the feasible integer solutions.)
(b) Find the
extreme points of the convex hull
and calculate their objective values.
Extreme point 1:
Extreme point 2:
Extreme point 3:
Extreme point 4:
Extreme point 5:
Extreme point 6:
(c) Draw an isocost line that passes through the point (
x
= 5
, y
= 0) and find the direction
of optimization.
(d) Provide the optimal solution and optimal objective function value.
Optimal solution:
x
=
y
=
Optimal objective value:
Assignment 6
2
x
y
Assignment 6
3
Question 2:
(20 points) Spencer Enterprises is attempting to choose among a series of new
investment alternatives. The potential investment alternatives, the net present value of the
future stream of returns, the capital requirements, and the available capital funds over the
next three years are summarized as follows:
Alternative
Net Present Value ( )
Year 1
Year 2
Year 3
Limited warehouse expansion
4000
3000
1000
4000
Extensive warehouse expansion
6000
2000
1500
1800
Test market new product
10500
2500
3500
3500
Advertising campaign
4000
6000
4000
5000
Basic research
8000
5000
1000
4000
Purchase new equipment
3000
1000
500
900
Capital funds available
10500
7000
8750
(a) Develop an optimization model for maximizing the net present value (Do not solve it
in Excel).
(b) Assume that only one of the warehouse expansion projects can be implemented. How
do you model this restriction?
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Assignment 6
4
Question 3:
(10 points) An Electrical Company has two manufacturing plants. The cost
in dollars of producing an Amplifier at each of the two plants is given below. The cost of
producing
Q
1
Amplifiers at the first plant is:
65
Q
1
+ 4
Q
2
1
+ 90
and the cost of producing
Q
2
Amplifiers at the second plant is
20
Q
2
+ 2
Q
2
2
+ 120
The company needs to manufacture at least 60 Amplifiers to meet the received orders. Pro-
duction time required for the Amplifiers at these plants is 6 and 8 hours per unit, respectively.
Currently, there are 260 and 220 hours available at these two plants, respectively. Formulate
an optimization model to find the optimal production quantity of Amplifiers at each plant
that minimizes the total production cost.
(Do NOT solve the model.)