hw-2
.pdf
keyboard_arrow_up
School
University of California, Los Angeles *
*We aren’t endorsed by this school
Course
MISC
Subject
Industrial Engineering
Date
Dec 6, 2023
Type
Pages
3
Uploaded by LieutenantSnow10841
IE 310: Deterministic Models in Optimization
HW 2
•
Each student should submit an individual homework.
•
Indicate the name of your collaborator in the first page of the submission.
•
State problem numbers clearly in the margin.
•
Write clearly. Illegible submissions will not be graded.
•
Submit your HW via Gradescope -
https://www.gradescope.com/
.
•
While submitting, ensure that you match the question number to the page in your submission.
•
Submission deadline is indicated in Gradescope. Late submissions by up to 3 hours will be
accepted.
•
Other solutions sources are
NOT
permitted.
•
Plagiarism will be dealt with severely.
No credit will be awarded for the entire homework
(even if part of the solution for a problem is plagiarized).
1.
(a) (
points: 3
) For each of the following constraints, draw a separate graph to show the
nonnegative solutions that satisfy this constraint (by shading).
i. 3
x
1
+
x
2
≤
6
ii. 3
x
1
+ 4
x
2
≤
12
iii.
x
1
+
x
2
≥
1
(b) (
points: 1
) Now combine the above constraints into a single graph to show the feasible
region for the entire set of constraints plus nonnegativity constraints.
(c) (
points: 1
) Can you change the RHS of one of the three constraints to make it redun-
dant (i.e., any (
x
1
, x
2
) that satisfies the other two constraints along with non-negativity
constraints will also satisfy the modified constraint)?
(d) (
points: 1
) Can you change the RHS of one of the three constraints to make it infeasi-
ble (i.e., there are no (
x
1
, x
2
) satisfying all three constraints along with non-negativity
constraints simultaneously)?
2. Consider the following objective function for a linear programming model:
max
Z
= 3
x
1
+ 2
x
2
(a) (
points:
3
) Draw a graph that shows the corresponding objective function lines for
Z
= 6,
Z
= 12 and
Z
= 18.
(b) (
points:
1.5
) Find the slope-intercept form of the equation for each of these three
objective function lines, i.e., write the equation as
x
2
=
mx
1
+
c
and identify
m
and
c
.
1
3. The Primo Insurance Company is introducing two new product lines: special risk insurance
and mortgages. The expected profit is $2 per unit on special risk insurance and $5 per unit
on mortgages.
Management wishes to establish sales quotas for the new product lines to
maximize total expected profit. The work requirements are as follows:
Department
Special Risk
Mortgage
Work-hours available
(Work hrs per unit)
(Work hrs per unit)
Underwriting
3
2
2400
Administration
0
1
800
Claims
2
0
1200
(a) (
points: 5
) Formulate a linear programming model for this problem.
(b) (
points: 2
) Use the graphical method to solve this model.
4. The following table summarizes the key facts about two products,
A
and
B
, and the resources
Q, R, S
needed to produce them.
Resource
Product A
Product B
Amount of resource available
(Resource Usage
(Resource Usage
per gallon produced)
per gallon produced)
Q
1
2
2
R
2
1
2
S
3
3
5
Profit per gallon
2
3
(a) (
points: 5
) Formulate a linear programming model to maximize the profit by making
suitable number of gallons of products
A
and
B
.
(b) (
points: 2
) Use the graphical method to solve this model.
5. The shaded area in the following graph represents the feasible region of a linear programming
problem whose objective function is to be maximized.
Label each of the following statements as TRUE or FALSE, and then justify your answer
based on the graphical method. In each case, give an example of an objective function that
illustrates your answer.
2
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