TEST 1. LINEAR PROGRAMMING. (10 Marks)

Direction: Read, Analyze and calculate what are required.

A small company builds two types of garden chairs.

Type a requires 2 hours of machine time and 5 hours of craftsman time.

Type b requires 3 hours of machine time and 5 hours of craftsman time.

Each day there are 30 hours of machine time available and 60 hours of craftsman time. The profit on each type a chair is 60 BD and on each type b chair is 84 BD.

Formulate the appropriate linear programming problem and solve it graphically to obtain the optimal solution that maximizes profit.

Use:

x = number of type chair a

y = number of type chair b

TEST 2. LINEAR REGRESSION. (10 Marks)

Direction: Read, Analyze and calculate what are required.

The Blood pressures, p mmHg, and the ages, t years of 6 hospital patients are shown in the table below.

Patient

A

B

C

D

E

G

t

42

22

34

45

27

60

p

98

130

120

88

80

135

1- Find the equation of the regression line of p on t. (8 Marks)

2- Use your line to estimate the blood pressure of a 40 year old patient..(2 Marks)

TEST 3. DECISION ANALYSIS. (10 Marks)

Direction: Read, Analyze and calculate what are required

Mary is considering the possibility of opening a small dress shop on Avenue, a few blocks from the university. She has located a good mall that attracts students. Her options are to open a small shop, a medium-sized shop, or no shop at all. The market for a dress shop can be good, average, or bad. The probabilities for these three possibilities are 0.2 for a good market, 0.5 for an average market, and 0.3 for a bad market. The net profit or loss for the medium-sized and small shops for the various market conditions are given in the following table. Building no shop at all yields no loss and no gain.

Alternative

Good Market

Average Market

Bad Market

Small shop

30,000

75,000

-40,000

Medium Sized shop

55,000

80,000

-60,000

No shop

0

0

0

a. Calculate the EMV criterion (2Marks)

b. Prepare the EVPI. (4 Marks)

c. Develop the opportunity loss table for this situation. What decisions would be made using the minimum EOL criterion?

(4 Marks)

TEST 4. ASSINGMENT MODEL. (10 Marks)

Direction: Read, Analyze and Calculate what required.

Five jobs J1, J2, J3,J4 and J5 are to be assigned to five persons P1,P2, P3 ,P4 and P5. The processing costs are given in the following matrix.

Find the optimal assignment which will lower the total processing cost.(2 marks per optimal assignment X 5=10 marks)

Jobs

Person

J1

J2

J3

J4

J5

P1

32

38

40

28

40

P2

40

24

28

21

36

P3

41

27

33

30

37

P4

22

38

41

36

36

P5

23

33

40

35

39

TEST 5. LINEAR PROGRAMMING .(10 Marks)

Direction: Read, Analyze and Calculate what required.

A company has fixed costs of $200,000 and produces one product with a selling price of $80.00 and a variable cost of $50.00 per unit. The maximum factory capacity is 30,000 units and it anticipates selling 20,000 units.

a- Create the mathematical model that represents the profit. (2 marks)

b-How much profit will they make at the present level of operation? (2 marks)

c-How much tables must the company sells to break even? (2 marks)

d-Determine the sales unit that the firm will have to reach if it is to make $20,000 profit per period. (2 marks)

e-How much profit will they make if sales increase to the maximum that the factory can supply? (2 marks)