Operations Research Answers

A transportation problem involves the following costs, supply, and demand.

To

From 1 2 3 4 Supply

1 $500 750 300 450 12

2 650 800 400 600 17

3 400 700 500 550 11

Demand 10 10 10 10

Required:

i. Find the initial solution using the northwest corner method, the minimum cell cost

method, and Vogel's Approximation Method. Compute total cost for each.

ii. Using the VAM initial solution, find the optimal solution using the modified distribution

method (MODI).

Consider the following transportation problem:

Store 1 Store 2 Store 3 Store 4 Supply

Plant 1 19 30 50 10

7

Plant 2 70 30 40 60 9

Plant 3 40 8 70 20 18

Demand 5 8 7 14 34

Required:

i. Set Up The Transportation Tableau For This Problem And Determine The InitialSolution

Using The Minimum Cell Cost Method.

ii. Solve Using MODI

iii. Formulate This Problem As A Linear Programming Model.

Consider the following transportation problem:

Store 1 Store 2 Store 3 Store 4 Supply

Plant 1 19 30 50 10

7

Plant 2 70 30 40 60 9

Plant 3 40 8 70 20 18

Demand 5 8 7 14 34

Required:

i. Set Up The Transportation Tableau For This Problem And Determine The InitialSolution

Using The Minimum Cell Cost Method.

ii. Solve Using MODI

iii. Formulate This Problem As A Linear Programming Model.

A company produces two types of products say type A and type B. Product A is of superior quality and product B is of a lower quality. Respective profits for the two types of products are BIRR 40 and BIRR 30.

The data on the resource required, availability of resources are given below

Requirement

Capacity available per month

Product A

Raw materials 120 kg

Machining time5 hrs/piece

Assembly 4 man-hour

Product B

Raw materials 60 kg

Machining time 8 hrs/piece

Assembly 3 man-hour

-Raw materials (kg) Product A and Product B Capacity available per month is 12000

-Machining time hrs/piece Product A and Product B Capacity available per month is 600

-Assembly man-hour Product A and Product B Capacity available per month is 500

Required:

  i. Formulate the problem as LPP?

ii. Solve using Simplex method

1.     Consider the following transportation problem:

Store 1

Store 2

Store 3

Store 4

Supply

Plant 1

19

30

50

10

7

Plant 2

70

30

40

60

9

Plant 3

40

8

70

20

18

Demand

5

8

7

14

34

Required:

          i.           Set Up The Transportation Tableau For This Problem And Determine The InitialSolution Using The Minimum Cell Cost Method.

        ii.           Solve Using MODI

      iii.           Formulate This Problem As A Linear Programming Model.

minimize Z=x₁+x₂+x₃

subject to x₁-3x₂+4x₃=5

x₁-2x₂<_3

2x₂- x₃>-4 x₁,x₃>-0 and x₃ is unrestricted