EM 602 FINAL EXAM NJIT

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:
Ø Identify / define the variables that are used in your model
Ø List any assumptions
Ø 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

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

.20

.05

Fair

.50

.30

.12

Critical

.51

.25

.20

Improved

Unimproved

Dead

Good

.06

.03

.01

Fair

.03

.02

.03

Critical

.01

.01

.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.

Consider
a patient who enters the hospital in good condition. On average, how many days does this
patient spend in the hospital?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 tomorrow’s hospital census (how many patients in good,
critical and fair condition, total)?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)?What
fraction of patients who enter the hospital in good condition, will leave
in improved condition?

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

Cost per truck from warehouse to Sales
District Sales Districts

Monthly Capacity(number of truck loads)

Monthly Leasing Cost

WAREHOUSE

1

2

3

4

A

$170

$40

$70

$160

200

$7,750

B

$150

$195

$100

$10

250

$4,000

C

$100

$240

$140

$60

300

$5,500

Monthly Demand (truck loads)

100

90

110

60

5. Newcor’s 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:

INGOTWEIGHT COST PER TON CARBON% MOLYBDENUM%

1 5
tons $350 5 3

2 3
tons $330 4 3

3 4
tons $310 5 4

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 COST PER TON CARBON% MOLYBDENUM%

1 $500 8 6

2 $450 7 7

3 $400 6 8

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