Assignment 5(1)
pdf
keyboard_arrow_up
School
University of Texas, Dallas *
*We aren’t endorsed by this school
Course
3333
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
4
Uploaded by AdmiralMule126
Assignment 5
1
Question 1.
(40 points) You are provided with the following linear program:
min
z
= 3
x
+
y
s.t.
y
−
0
.
5
x
≥
1
y
+
x
≥
3
x
≤
3
y
≤
4
x, y
≥
0
(a) On the following page, use the graphical solution method to identify the feasible region.
Use the scale 0.5 by 0.5 for each small square.
(b) Find the
feasible
extreme points and calculate their objective values.
Extreme point 1:
Extreme point 2:
Extreme point 3:
Extreme point 4:
Extreme point 5:
(c) Draw an isocost line that passes through the point (
x
= 2
, y
= 3) and find the direction
of optimization.
(d) Provide the optimal solution and optimal objective value.
Optimal solution:
x
=
y
=
Optimal objective value:
Assignment 5
2
x
y
Assignment 5
3
Question 2.
(20 points) A beverage cans manufacturer makes 3 types of soft drink cans
needed for the beverage producers to fill soft drinks of three different volumes. The maximum
availability of the machines’ time allotted per day is 90 hours and the supply of metal is
limited to 120 kg per day. The following table provides the details of the input needed to
manufacture one batch of cans.
Cans
Large
Medium
Small
Maximum
Metal (kg)/batch
9
6
5
120
Machines’ Time (hr)/batch
4.4
4.2
4
90
Profit/batch
50
45
42
The manufacturer is interested in maximizing the total profit per day. The sensitivity report
provided below was generated using the Excel Solver to determine the optimal solution to
this problem. Using the sensitivity report, answer the following questions:
(a) Optimal production quantity of small can per day:
(b) Optimal profit per day:
(c) Will the current optimal solution stay optimal if the unit profit of large can increases
to 60? (Yes or No)
(d) Will the current optimal solution stay optimal if the unit profit of small can decreases
to 40? (Yes or No)
(e) Will the current optimal solution stay optimal if we add a constraint that says pro-
duction quantity of large can per day should be at least 5? (Yes or No)
(f) Will the shadow price of the constraint related to the supply of metal remain valid if
we increase the available supply to 130 kg per day? (Yes or No)
(g) Calculate the effect on the total profit of decreasing the supply of metal to 115 kg per
day.
(h) Calculate the effect on the total profit of increasing the machine available time to 95
hours per day.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Assignment 5
4
Question 3.
(20 points) Ethan Steel, Inc.
has three factories that manufacture steel
components for three different rail projects located at three different sites.
They want to
determine how many steel components must be transported from each factory to each project
site.
The demand for the steel components for the three projects, A, B and C, are 2500,
3000 and 4500, respectively. The production and shipping details are as below:
Production details:
Factory
Maximum capacity
1
3000
2
5000
3
3000
Shipping details (with per-unit shipping cost in dollars):
Project
Factory
A
B
C
1
7
8
2
2
6
5
4
3
1
9
6
Develop a linear programming optimization model to determine the distribution plan (from
factories to projects) that minimizes the total transportation cost.
(Do NOT solve the
model.)