Operations Research Answers

. If the promotional budget is limited to $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media, and what is the total audience reached?

Minimize Z = 0.2x1+ O.lx2 + 0.3x3

Subject to constraint

0. Sx1+ 0.2x2 + 0.7x3 = 0.420

0. 3x1+ 0.2x2 + O.Sx3 ;:::: 0.280

Xv Xz, X3 ;:::: 0.

(i) W1ite second initial basic solution of the p1imal problem using M-Method.

(ii) Solve the dual from optimal Primal table calculated in (i).

Solve the ILLP given below by graphical method :

Maximum Z = 95x1 + 100x2

Subject to the constraints

5x1 + 2x2 ≤ 20

x1 ≥ 3

x2 ≤ 5

x1 , x2 are non - negative Integers

Write the dual of the following LPP :

Minimize Z = 16x1 + 9x2 + 21x3

Subject to the constraints

x1+ x2 + x3 = 16

2x1 + x2+ x3 ≥ 12

x1, x2 ≥ 0

x3 - unrestricted.

Use dual simplex method to solve the following LPP .

Min z = x1 + 2x2 + 3x3

Subject to

x1 - x2 + x3 ≥ 4

x1 + x2 + 2x3 ≤ 8

x1 - x3 ≥ 2

x1, x2, x3 ≥ 0 .

Use the simplex method to solve the following LPP .

Max z = 4x1 + 3x2

Subject to

2x1 + X2 ≤ 1000

x1 + x2 ≤ 800

x1 ≤ 400

x2 ≤ 700

x1 , x2 ≥ 0

A firm makes two products A and B has a total production capacity of 9 tonnes per day , with A and B utilising the same production facilities . The firm has a permanent contract to supply at least 2 tonnes of A per day to another company. Each tonne of A requires 20 machine hours of production time and each tonne of B required 50 machine hours of production time . The daily maximum possible number of machine hours is 360 . All the firm's output can be sold and the profit made is Rs. 80 per tonne of A and Rs. 120 per tonne of B . Formulate the problem of maximizing the profit as an LPP and solve it graphically

A television repairman finds that the time spent on his jobs has an exponential distribution with a mean of 30 minutes . If he repairs sets in order in which they come in , and if arrival of sets follows a Poisson distribution approximately with an average rate of 10 per 8 hours day , what is the repairman's expected ideal time each day, how many jobs are ahead of the average set just brought in?

If the availability and requirements of a balanced transportation problem are integers , the optimal solution to the problem will have integer value . Justifie the statement are true and false ? Give a proofs or a counter example

A contractor has to supply 10,000 bearings per day to an automobile manufacturer . He finds that when he starts production run, he can produce 25,000 bearings per day. The cost of holding a bearing in stock for one year is Rs. 2 and the set up cost of a production run is Rs. 180 . Find the EOQ . How frequently should the production run he made ?