The document details several linear programming problems involving logistics and resource allocation. It covers the optimization of transportation costs for parts distribution, project funding for maximizing votes, advertisement campaign planning within a budget, sales region assignments among salespersons, and specific constraints for resource shipment. Each section requires the formulation of decision variables, objective functions, and constraints without solving them.

1. 1. A logistics specialist for Charm City Inc. must distribute
cases of parts from 3 factories to 3 assembly plants. The
monthly supplies and demands, along with the per-case
transportation costs are:
Assembly Plant
1
2
3
Supply
_____________________________________________________
_____________
A
6
10
14

2. 200
Factory
B
2
2
6
400
C
2
8
7
200
_____________________________________________________
_____________
Demand
220
320

3. 200
The specialist wants to distribute at least 100 cases of parts
from factory B to assembly plant 2.
(a) Formulate a linear programming problem to minimize total
cost for this transportation problem.
(b) Solve the linear programming formulation from part (a) by
using either Excel or QM for Windows. Find and interpret the
optimal solution and optimal value. Please also include the
computer output with your submission.
The following questions are mathematical modeling questions.
Please answer by defining decision variables, objective
function, and all the constraints. Write all details of the
formulation.
Please do
NOT
solve the problems after formulating.
2. A congressman’s district has recently been allocated $45
million for projects. The congressman has decided to allocate
the money to four ongoing projects. However, the congressman
wants to allocate the money in a way that will gain him the most

4. votes in the upcoming election. The details of the four projects
and votes per dollar for each project are given below.
Project
Votes/dollar
________________________
Parks
0.07
Education
0.08
Roads
0.09
Health Care
0.11
Family Welfare
0.08
In order to also satisfy some local influential citizens, he must
meet the following guidelines.

5. - None of the projects can receive more than 30% of the total
allocation.
- The amount allocated to education cannot exceed the amount
allocated to health care.
- The amount allocated to roads must be equal to or more than
the amount spent on parks.
- All of the money must be allocated.
Formulate a linear programming model for the above situation
by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each
constraint represents.
Note: Do NOT solve the problem after formulating.
3. An ad campaign for a trip to Greece will be conducted in a
limited geographical area and can use TV time, radio time,
newspaper ads, and magazine ads. Information about each
medium is shown below.
Medium

6. Cost Per Ad
Number Reached
TV
8500
12000
Radio
1800
4000
Newspaper
2400
5500
Magazine
2200
4500
The number of TV ads cannot be more than 4. Each of the media
must have at least two ads. The total number of Magazine ads
and Newspaper ads must be more than the total number of Radio
ads and TV ads. There must be at least a total of 12 ads. The
advertising budget is $50,000. The objective is to maximize the
total number reached.
Formulate a linear programming model for the above situation
by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each
constraint represents.

7. Note: Do NOT solve the problem after formulating.
4. The Charm City Vacuum Company wants to assign three
salespersons to three sales regions. Given their experiences, the
salespersons are able to cover the regions in different amounts
of time. The amount of time (days) required by each salesperson
to cover each region is shown in the following table:
Region (days)
Salesperson
I
II
III
________________________________________
A
11

8. 18
12
B
11
15
14
C
10
14
16
However, because of his health reason, salesperson C does not
want to be assigned to region II.

9. The Company wants to assign either salesperson A or
salesperson C to region I. The objective is to minimize total
time of covering the three sales regions.
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each
constraint represents.
Note: Do NOT solve the problem after formulating.
5. To (cost)
From
1 2 3
Supply
_____________________________________________
A $ 6 $9 $

10. M
130
B 12 3 5 70
C 4 8 11 100
Demand
80 110 60
Assume that the following special situations occur. Determine
one constraint for each of these special situations. The
conditions are independent of one another.
(a) No shipment is possible from origin A to destination 3.
(b) At most 50 units can be shipped from origin C to destination
2.
(c) Destination 1 must receive at least 40 units from origins A
and B.