Determine the critical path

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Reference no: EM131054

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.

  1. Formulate the given problem as a linear programming problem.
  2. 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

1/2

3/4

0

0

37.5

0

S2

0

-2/3

0

1/2

0

-1

5

20

x2

0

1

1/2

1/4

0

1/3

57.5

 

Zj

10

20

15

25/3

0

20/3

m

 

Cj-Zj

0

0

0

-25/3

0

-20/3

 

i. Set up the initial simplex tableau for the above problem

ii. How many kilograms of each cookie should be baked?

iii.Determine the value of m

iv. Identify any ingredient that is not fully utilized. State the amount unused.

v. How would the optimum solution change if the RHS value for the first resource increases by 10 units?

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.

           b. Find the total inventory cost associated with the optimal order quantity.

           c. What is the reorder point?

           d. What is the cycle time?

Question 3

  1. 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

X

Y

Z

A

8

7

5

B

6

8

9

C

9

6

5

  1. 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

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.

b. Determine the critical path and the expected project completion time.

Reference no: EM131054

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