# Maryland International College

Maryland International College

MBA Program

Course Title: Quantitative Analysis (Management Science)

Course Code: MBA-652

Submission Date: June 19/2022

Marks: 50%

Individual Assignment

Full Name ID No. Email Phone No.

1. Discuss the relevance of quantitative analysis for the improvement of the quality of

management decision making using a manufacturing firm as an example.

2. A dealer wishes to purchase a number of fans and sewing machines. He has only 5760 ETB to

invest and has space for almost 20 items. A fan costs him 360 ETB and sewing machine 240

ETB. His expectation is that he can sell a fan at profit of 44 ETB and a sewing machine at a

profit of 36 ETB. Assuming that he can sell all the items that he can buy, how should he invest

his money in order to maximize his profit. (Note: ETB = Ethiopian Birr)

a. Formulate it as a linear programming problem (LPP).

b. Use the graphical method to solve it.

c. Solve the Linear programming problem using simplex method.

3. A firm produces three products Z, Y, and X, each of which passes through three departments:

Fabrication, Finishing and Packaging. Each unit of product Z requires 3, 4 and 2 hours; a unit of

Y requires 5, 4 and 4 hours while each unit of product X requires 2, 4, 5 hours respectively in

the three departments. Every day, 60 hours are available in fabrication department, 72 hours in

the finishing department and 100 hours in the packaging department. If the unit contribution of

product Z is ETB 5, of product Y is ETB 10, and of product X is ETB 8, determine the number

of units of each of the products, which should be made each day to maximize the total

contribution. Also determine if any capacity would remain unutilised.

a. Write the formulation for this linear program.

b. Solve the Linear programming problem using simplex method.

4. A product is manufactured by four factories A, B, C and D. The unit production costs in them

are ETB 2, ETB 3, ETB 1 and ETB 5 respectively. Their production capacities are 50, 70, 30

and 50 units respectively. These factories supply the product to four stories, demands of which

are 25, 35, 105, and 20 units respectively. Unit transportation cost in ETB for each factory to

each store is given in the table below.

Stores

1 2 3 4

A 2 4 6 11

Factories B 10 8 7 5

C 13 3 9 12

D 4 6 8 3

Determine the transportation plan to minimize the total production-cum-transportation cost by

using:

a. Least cost method

b. Vogel’s Approximation Method (VAM) for initial basic feasible solution

5. A company is producing a single product and is selling it through five agencies situated in

different cities. All of a sudden, there is a demand for the product in another five cities not

having any agency of the company. The company is faced with the problem of deciding on how

to assign the existing agencies to despatch the products to needy cities in such a way that the

total travelling distance is minimized. Determine the optimum assignment schedule. The

distance between the surplus and deficit cities (in K.M.) is given below.

Surplus Cities

Deficit Cities

A

1 B

1 C

1 D

1 E

1

A 7 5 9 8 11

B 9 12 7 11 10

C 8 5 4 6 9

D 7 3 6 9 5

E 4 6 7 5 11

6. Consider following data. Draw activity on arc (AOA) network diagram. Find out critical path,

expected duration, slack, total and independent floats. What is the probability that it would be

completed in:

a. 14 weeks and

b. 18 weeks?

Activity Predecessor

Activity Optimistic Most

Likely Pessimistic

A — 2 3 10

B — 2 3 4

C A 1 2 3

D A 4 6 14

E B 4 5 12

F C 3 4 5

G D, E 1 1 7

7. Consider the following data (ETB and days).

a. Draw activity network of the project.

b. Crash the activities step by step until all paths are critical.

Activity Normal Time Normal Cost Crash Time Crash Cost

1-2 20 600 17 720

1-3 25 200 25 200

2-3 10 300 8 440

2-4 12 400 6 700

3-4 5 300 2 420

4-5 10 300 5 600

4-6 5 600 3 900

5-7 10 500 5 800

6-7 8 400 3 700

8. An average annual consumption of a material is 18,250 units at a price of ETB 36.50 per unit.

The storage cost is 20% of an average inventory and the cost of placing an order is ETB 50.

How much quantity is to be purchased at a times?

9. The demand for a certain product is random. It has been estimated that the monthly demand of

the product has a normal distribution with a mean of 585 units. The unit price of product is ETB

37.5. Ordering cost is ETB 60 per order and inventory carrying cost is estimated to be 52.5

percent per year. Calculate economic order quantity (EOQ).

10. Given the data below, what is the simple linear regression model that can be used to predict

sales in future weeks?

Week 1 2 3 4 5

Sales 300 314 324 332 360