Assignment

Management Science Application Assignment 2015
BEC 2307 / INB 2307/ MKT 2307 / HLM 2307
Question # 01
A calculator company produces a scientific calculator and a graphing calculator. Longterm projections indicate an expected demand of at least 100 scientific and 80 graphing
calculators each day. Because of limitations on production capacity, no more
than 200scientific and 170 graphing calculators can be made daily. To satisfy a shipping
contract, a total of at least 200 calculators much be shipped each day.
If each scientific calculator sold results in a $2 loss, but each graphing calculator produces
a $5 profit, how many of each type should be made daily to maximize net profits?
Question # 02
A manufacturer produces three types of plastic fixtures. The time required for molding,
trimming, and packaging is given in the following table (Times are given in hours
per dozen fixtures.)
Process
Type A
Type B
Type C
Total Time
Available
Molding
1
2
3
2
12000
Trimming
2
3
2
3
1
4600
Packaging
1
2
1
3
1
2
2400
Profit
$ 11
$ 16
$ 15
-
How many dozen of each type of fixture should be produced to obtain a maximum profit?
Question # 03
The Munchies Cereal Company makes a cereal from several ingredients. Two of the
ingredients, oats and rice, provide vitamins A and B. The company wants to know how
many ounces of oats and rice it should include in each box of cereal to meet the minimum
requirements of 48 milligrams of vitamin A and 12 milligrams of vitamin B while
minimizing cost. An ounce of oats contributes 8 milligrams of vitamin A and 1 milligram
of vitamin B, whereas an ounce of rice contributes 6 milligrams of vitamin A and 2
milligrams of vitamin B. An ounce of oats costs $0.05, and an ounce of rice costs $0.03.
Formulate a linear programming model for this problem and solve using the simplex
method.
© M. R. Rajasuriya
Page 1
Management Science Application Assignment 2015
BEC 2307 / INB 2307/ MKT 2307 / HLM 2307
Question # 04
Determine the solution to the following transportation problem using appropriate
methods, where Oi and Dj represent i th origin and j th destination respectively.
O1
O2
O3
Demand
D1
10
12
8
6
D2
8
13
7
10
D3
5
6
10
15
D4
9
11
6
4
Supply
14
16
5
Question # 05
“Project control should always focus on the critical path.” Comment.
The following table lists the jobs of a network along with their time estimates.
i-j
Optimistic
1-2
1-6
2-3
2-4
3-5
4-5
5-8
6-7
7-8
3
2
6
2
5
3
1
3
4
Most
Likely
6
5
12
5
11
6
4
9
19
Pessimistic
15
14
30
8
17
15
7
26
28
a) Draw the project network.
b) Calculate the length and variance of critical path
c) What is the approximate probability that jobs on the critical path will be
completed by the due date of 41 days?
d) What is the approximate probability that jobs on the next most critical path
will be completed by the due date?
Question # 06
Consider a salon with one barber. Over an 8 hour day, an average of 26 people gets their
hair cut per day. It takes an average of 15 minutes to cut someone's hair (exponentially
distributed).
i.
ii.
How long does it take someone to get a haircut, from the time they walk in the
door until they are done?
completely analyze the system
© M. R. Rajasuriya
Page 2