Final Assignment: A soda producer makes and sells two products, Classic Cola and Diet Cola.

Instructions: Complete all problems. You can use either Solver, Lindo or excel to resolve
problems. Be sure to indicate all variables and explain all models. All work must
be done individually. You must turn in the template with answers incorporated.
The work should also be contained within the worksheets of the template or you
can submit a word document that illustrates your work. In each worksheet or word
document you must:
Identify / define the variables that are used in your model
List any assumptions
Highlight the answers and include the answers on the front (answer sheet) of
the template
1. (10 points) - A soda producer makes and sells two products, Classic Cola and Diet Cola.
If this company spends x1 dollars on promotion of Classic Cola in a particular western city, it
can sell 175 X1 0.75 12-packs of Classic Cola each week there. Moreover, if this company
spends x2 dollars on promotion of Diet Cola in a particular western city, it can sell 150X2
0.75 12-packs of Diet Cola each week there. Each 12-pack of Classic Cola sells for $4.00
and costs $01.20 to produce and ship to customers in this western city. Each 12-pack of Diet
Cola sells for $3.50 and costs $1.00 to produce and ship to customers in this western city. A
total of $20,000 is available for promotion each week in this city. The soda producer seeks to
maximize its weekly profit. Formulate and solve an appropriate optimization model to help
this soda producer identify the best promotional strategies for its two products.
2. (20 points) Periodic preventive maintenance is carried out on aircraft engines, where an
important component must be replaced. The number of aircraft scheduled for such
maintenance over the next 6 months is estimated at 200,180, 300,198,230, and 290,
respectively. All maintenance work is done in the month that parts are available, where a
used component may be replaced with a new or an overhauled component. The overhauling
of used components may be done in a local repair facility, where they will be ready for use at
the beginning of next month, or they may be sent to a central repair shop where a delay of 2
months (as such maintenance can occur in the third month) is expected. The repair cost in the
local shop is $120 per component. At the central facility, the cost is only $35 per component.
An overhauled component used in a later month will incur an additional storage cost of $1.50
per unit per month. New components may be purchased at $200 each in month 1, with a 5%
price increase every 2 months. A new component is available immediately (no delay).
Formulate a model to the problem and solve to determine the optimal schedule for satisfying
the demand for the component over the next 6 months. Also consider that the planning occurs
within the first month. So all parts are ordered in the first month to satisfy maintenance
requirements

1

3. (30 Pts) At the beginning of each day, a patient in a hospital is classified into one of three
conditions; good, fair, or critical. At the beginning of the next day, the patient will either
continue to be in the hospital and be in good, fair or critical condition or the patient will be
discharged in one of three conditions: improved, unimproved or dead. The transition
probabilities for these situations are as follows:
Good
Fair
Critical

Good
.65
.50
.51

Good
Fair
Critical

Improve
d
.06
.03
.01

Fair
.20
.30
.25

Critical
.05
.12
.20

Unimproved Dead
.03
.02
.01

.01
.03
.02

For example, a patient who begins the day in fair condition has a 12% chance of being in
critical condition the next day and a 3% chance of being discharged the next day in
improved condition.
a. Consider a patient who enters the hospital in good condition. On average, how
many days does this patient spend in the hospital?
b. This morning, there were 500 patients in good condition, 300 in fair condition,
and 200 patients in critical condition in the hospital. Tomorrow morning, the
following admissions will be made: 50 patients in good condition, 40 in fair
condition and 30 patients in critical condition. On the basis of this, predict
tomorrows hospital census (how many patients in good, critical and fair
condition, total)?
c. The hospitals daily admissions are as follows: 20 patients in good condition, 10
patients in fair condition and 10 patients in critical condition. On average, how
many patients of each type would you expect to see in the hospital (think steady
state conditions)?
d. What fraction of patients who enter the hospital in good condition, will leave in
improved condition?

22

4. Steco, a steel wholesaler, leases regional warehouses for its operation on a monthly basis.
Steco currently has a list of three potential warehouses that it can lease. The cost per month
to lease each warehouse is shown in table 1 below. There are four sales districts in Stecos
operation. The monthly demand (in truck load requirements) is indicated in table 1 as well as
the unit cost of sending a truck from a warehouse to a given district. Steco wants to know
which warehouses to lease and how many trucks to send from each warehouse to each
district that will minimize overall cost. Keep in mind that every warehouse does not have to
be used. Formulate an LP program and solve this problem. (10 pts)
Table 1
Monthly
Capacity
Monthly
Cost per truck from warehouse to Sales District (number of truck Leasing
Sales Districts
loads)
Cost
WAREHOUSE
A
B
C

1
$170
$150
$100

2
$40
$195
$240

3
$70
$100
$140

4
$160
$10
$60

Monthly
Demand (truck
loads)

100

90

110

60

200
250
300

$7,750
$4,000
$5,500

5. Newcors steel mill has received an order for 25 tons of steel. The steel must be 5% carbon
and 5% molybdenum by weight. The steel is manufactured by combining three types of metals;
steel ingots, scrap steel and alloys. Steel ingots can only be purchased in lot sizes of 1 at the
specified weights given in the table below. The ingot can be cut to the desired amount needed in
the process. The weight, cost per ton and chemical contents of each ingot is:
INGOT
CARBON%
1

WEIGHT
MOLYBDENUM%

COST PER TON
5 tons

$350
5
3
2

3 tons
$330
4

3
3

4 tons
$310
5

4
3

4

6 tons
$280
3

4
Unlimited amounts of alloys and scrap steel can be purchased. Scrap steel cost $100 per ton
and contains 3% carbon and 9% molybdenum. The cost per ton and chemical make up of the
alloys is:

ALLOY
MOLYBDENUM%
1
$500
2
$450
3
$400

COST PER TON

CARBON%
8
6
7
7
6
8

Determine the appropriate mixture of the steel components to minimize the cost of fulfilling
the requirements. 20 pts