Operations Research Answers

Find the initial basic feasible solution of the following transportation problem using North- West corner method:

P₁ P₂ P₃ P₄ Requirement

M₁ 19 11 23 11 11

M₂ 15 16 12 21 13

M₃ 30 25 16 39 19

Availability 6 10 12 15 113

Also, find the optimal solution.

Using graphical method, solve the game whose pay-off matrix is given as:

Player B

I II III IV

Player A I 1 3 -3 7

II 2 5 4 -6

A manufacturer has two products P₁ and P₂ , both of which are produced in two steps by machines M₁ and M₂. The process time per hundred for the products on the machines

M₁ M₂ Profit(in

thousand Rs.

per 100 units)

P₁ 4 5 10

P₂ 5 2 5

Available 100 80

hours

The manufacturer can sell as much as he can produce of both products. Formulate the problem as LP model. Determine optimum solution, using simplex method.

Consider the system of equations

2x₁+x₂+4x₃=11

3x₁+x₂+5x₃=14

feasible solution is x₁=2,x₂=3,x₃ =1.Reduce this feasible solution to a basic feasible solution.

While solving problems, clearly indicate which part of which question is being solved.

For the following matrix game, write down the equivalent LPPs for solving the game.

B

A= -1 2

1 0

Write the dual of the following LPP after reducing it to canonical form.

Min Z = 3x₁ + 4x₂ + 3x₃

Subject to

2x₁+4x₂ =12

5x₁+3x₃ ≥11

6x₁+ x₂ ≥ 8

x₁,x_2,x₃≥0