1. This Assignment is an Individual Assignment and consists of 7 pages including cover page and the statistical tables.

2. Answer all FIVE questions. All questions carry equal marks and the distribution of the marks for each question is given.

3. The hard copy of the answer booklet must be printed and must be submitted to your respective lecturer on or before 9 September 2013

Question 1

Melissa Bakery is preparing for the coming thanksgiving festival. The bakery plans to bake and sell its favourite cookies; butter cookies, chocolate cookies and almond cookies. A kilogram of butter cookies requires three cups of flour, one cup each of special ingredient and choc chip. A cup of special ingredient is added to five cups of flour together with three cups of choc chic to bake a kilogram of chocolate cookies. For baking a kilogram of almond cookies; Melissa requires four cups of flour, a cup of special ingredient and two cups of choc chip. However, each day the bakery can only allocate at most 400 cups of flour, 100 cups of special ingredient and 210 cups of choc chip to bake the cookies. Melissa estimates a daily profit of RM10 for butter cookies, RM20 for chocolate cookies and RM15 for almond cookies. The bakery wishes to maximize the daily profit.

a. Formulate the given problem as a linear programming problem. [4 marks]

b. The following is the final simplex tableau for the above problem:

Cj 10 20 15 0 0 0
Solution Mix x1 x2 x3 S1 S2 S3 Quantity
10 x1 1 0

0 0 37.5
0 S2 0
0 -1 5
20 x2 0 1

Zj 10 20 15
Cj-Zj 0 0 0

i. Set up the initial simplex tableau for the above problem [6 marks]

ii. How many kilograms of each cookie should be baked? [3 marks]

iii. Determine the value of m [2 marks]

iv. Identify any ingredient that is not fully utilized. State the amount unused.
[2 marks]
v. How would the optimum solution change if the RHS value for the first resource increases by 10 units?
[3 marks]
[Total 20 marks]
Question 2

The Maju Supermarket stocks Munchies Cereal. Demand for Munchies is 4,000 boxes per year and the super market is open throughout the year. Each box costs $4 and it costs the store $60 per order of Munchies, and it costs $0.80 per box per year to keep the cereal in stock. Once an order for Munchies is placed, it takes 4 days to receive the order from a food distributor.

a. Find the optimal order quantity. [6 marks]

b. Find the total inventory cost associated with the optimal order quantity.
[6 marks]

c. What is the reorder point? [4 marks]

d. What is the cycle time? [4 marks]

[Total 20 marks]

Question 3

a. A company has three factories A, B and C which supply units to warehouses X, Y and Z every month. The capacities of the factories are 60, 70 and 80 units at A, B and C respectively. The requirements of X, Y and Z per month are 50, 80 and 80 units respectively. Transportation costs per unit in ringgits are given in the following table. How many units should ship from each factory so that the total cost is minimum? Use VAM method for the initial solution and Stepping Stone method to obtain an optimal solution.

Factories Warehouses
A 8 7 5
B 6 8 9
C 9 6 5

[10 marks]


b. The Dean of the Faculty of Science at City Science University has decided to
apply the Hungarian method in assigning lecturers to courses for the next semester. As a criterion for judging who should teach each course, the Dean reviews the past two years’ teaching evaluations (which were filled out by students). Since each of the four lecturers taught each of the four courses at one time or another during the two-year period, the Dean is able to record a course rating for each lecturer. These ratings are shown in the table below. Find the best assignment of lecturers to courses to maximize the overall teaching rating.

Lecturer Biology Chemistry Physics Applied Sciences
Nora Bee 90 65 95 40
Lee Along 70 60 80 75
Rama Sundar 85 40 80 60
Charles Abby 55 80 65 55

[10 marks]

[Total 20 marks]

Question 4

The project of building a backyard swimming pool consists of eight major activities and has to be completed within 19 weeks. The activities and related data are given in the following table:
Activity Immediate predecessor Activity time (weeks)
A - 3
B - 6
C A 2
D B,C 5
E D 4
F E 3
G B,C 9
H F,G 3

a. Draw a network diagram for this problem. [6 marks]

b. Determine the critical path and the expected project completion time.
[6 marks]

c. Assume the project variance is 4 weeks2.
i. What is the probability that all the activities are completed
within 19 weeks? [4 marks]

ii. When is the due date if there is a 90% of completing
all the activities?
[4 marks]

[Total 20 marks]

Question 5

The Operations Research Unit of a Fast Moving Consumer Goods (FMCG) company had generated the following payoff table, which is given below.

State of Business Nature
Decision s1 s2 s3
d1 10 8 6
d2 14 15 2
d3 7 8 9

a. What decision should be made by the optimistic decision maker?
[4 marks]

b. What decision should be made by the conservative decision maker?
[4 marks]

c. What decision should be made under minimax regret? [4 marks]

d. If the probabilities of s1, s2, and s3 are 0.2, 0.4 and 0.4 respectively, then what decision should be made under expected value? [4 marks]

e. What is the Expected Value of Perfect Information (EVPI)? [4 marks]

[Total 20 marks]

End of Questions

Posted Date: 8/4/2013 9:00:10 PM | Location : Malaysia

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