Operations Research Answers

At a one man barber shop, customers arrive according to poison distribution with a

mean arrival rate of 5 per hour and hair cutting time was exponentially distributed

with an average hair cutting time was exponentially distributed with an average hair

cut taking 19 minutes. It is assumed that because of excellent reputation, customers

were always willing to wait. Calculate the following

a. Average number of customers in the shop and average numbers waiting for a hair

cut

b .Percentage of time arrival can walk in right without having to wait

c. The percentage of customers who have to wait before getting into the barber’s chair

Use dual Simplex method to solve the following LPP.

Max Z= -3X1-2X2

Subject to x1+x2>1

X1+X2<7

X1+2X2>10

X2<3

X1,X2>0

1)    Complete the regularization of the following primal problem

            Min Z = 15x₁  +  15x₂

               s.t       3x₁ + 2x₂ > 2

                          7x₁ + 2x₂ = 6

                          5x₁ + 7x₂ < 4

                           x₁ ,  x₂ > 0

For model:

3x1+2x2+7x3+5x4+2x5>= 13000

2x2+x4+2x5+3x6>=20000

F(c)=0,2x1+0,1x2+0,2x3+0,3x4+0,4x5+0x6

Build a dual model, solve using the graphical method

Solve the following LPP using dual simplex method: Max Z= -3x1- x2,

Subject to: x1+x2 ≥ 1, 2x1+3x2 ≥ 2, x1,x2 ≥ 0.

Placid company makes 3 production components A, B, C using 3 machines Cutting, Polishing and Packaging whose allocated and available hours are not more than 96hrs, 40hrs and 60hrs respectively. Product A spends 6 hours on cutting machine, 2 hours on polishing and 5 hours on packaging machine. Product B goes through 8 hours of cutting, 1 hour of polishing and 3 hours of packaging. Product C takes 4 hours on cutting machine, 4 hours of polishing and 2 hours of packaging. Contribution margins for each component product are N2, N5 and N8.

Use the Simplex Algorithm to determine how many of each component the Placid Company will make to maximize contribution

A manufacturer makes two products, doors and windows. Each must processed through two work areas. Work area #1 has 60 hours of available production time. Work area #2 has 48 hours of available production time. Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2. Profit is $8 per door and $6 per window