ISDS 514 Practice Problems for Exam 1 Dr. Z. Drezner

ISDS 514 Practice Problems for Exam 1 Dr. Z. Drezner

Question #1

You plan to buy and sell six products this year and three additional years. You sell all the products you buy. Listed in the table are the percent increase in sales from one year to the next and profit per unit sold. You need to determine how many units to order this year (the orders for the next three years are automatically determined by the percentage increase in the table). You should order no more than 500 units of each of the 6 products in the first year. The total order over four years should be at least 500 units for each product and no more than 5000 for all six products combined. Your objective is to maximize profit over the four years. How many units should be ordered for each product in the first year? How will your answer change if you are not allowed to order more than 500 units of each product in any of the 4 years?

Product 1 / 2% / $18
Product 2 / 4% / $12
Product 3 / 3% / $16
Product 4 / 5% / $13
Product 5 / 4% / $10
Product 6 / 2% / $17

Question #2

Solve the following PERT problem and answer the following questions:

1.  What is the expected duration of the project?

2.  What is the critical path?

3.  What is the standard deviation of the duration of the project?

4.  If you consider 3.5 standard deviations as "safe" what duration will you commit yourself to?

5.  What is the probability that the duration of the project will exceed 80 days?

Activity / Predecessors / Optimistic / Most likely / Pessimistic
A / D / 12 / 12 / 18
B / F,I / 2 / 8 / 8
C / B,H / 5 / 12 / 19
D / -- / 3 / 4 / 5
E / B,H / 12 / 13 / 14
F / A,D,J / 8 / 8 / 14
G / C,E / 10 / 12 / 20
H / F,J / 12 / 15 / 18
I / -- / 15 / 17 / 19
J / D,I / 12 / 14 / 16

Question #3

You need to purchase airplanes for your fleet. There are four types of airplanes you consider. The data is given in the table below. Two of them are used for short flights and two are used for long flights. In the table you have the number of flights that will be flown per day, the cost of each airplane in millions of dollars, and the number of passengers an airplane can carry.

Airplane: / A / B / C / D
Short / Short / long / long
Flighs/day / 3 / 3 / 1 / 1
cost / 8 / 10 / 25 / 28
capacity / 50 / 60 / 320 / 350

You wish to be able to serve at least 60,000 passengers per day, at least 30,000 passengers in short flights, and 20,000 passengers in long flights. You wish to buy at least 20 airplanes of each type and minimize your total cost.

a. Find a solution when the number of airplanes of each type does not have to be integer.

b. Find the solution when the number of airplanes must be integer.

Question #4

There are four processes that use three ingredients and produce two products. In the table below the following is given: the number of units of each ingredient used in each process and the unit cost for each ingredient; the number of products produced by each process and the revenue per product; the processing cost (in addition to the cost of the ingredients), and the capacity available for each process. Also, you cannot produce more than 3000 products of each type. Find the number of times each process should be run and what is your maximum profit. The number of processes does not have to be integer.

Ing1 / Ing2 / Ing 3 / Prod1 / Prod2 / Add’l cost / Capacity
Proc1 / 3 / 7 / 4 / 10 / 5 / $3 / 130
Proc2 / 5 / 2 / 3 / 5 / 3 / $2 / 170
Proc3 / 7 / 6 / 5 / 7 / 7 / $5 / 100
Proc4 / 8 / 3 / 3 / 8 / 5 / $4 / 180
Cost / $3 / $5 / $4 / revenue / $8 / $12