Operations Research Answers

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 ?

The optimal solution of an ILLP can be obtained by rounding off the optimal solution of its LP relaxation .

The optimal solution for the following LPP is Z* = 30 :

Max Z = X1 - X2 + 3X3

Subject to X1 + X2 + X3 less than or equal to 10

X1, X2, X3 greater than or equal to zero .

Healthy Snacks Co. produces snack mixes. Recently, the company has decided to introduce a new snack mix that has peanuts, raisins, pretzels, dries cranberries, sunflower seeds and pistachios. Each bag of the new snack is designed in order to hold 250 grams of the snack. The company has decided to market the new product with an emphasis on its health benefits. After consulting nutritionists, Healthy Snacks decides to mix the ingredients so that the snack has the following specifications:

 Three custom officers check the luggage of the passengers of an airport. The 

passengers are found to arrive at an average rate of 30 per 8 hours a day. The amount 

of time a custom officer spends with the passenger is found to have an exponential 

distribution with mean service time 32 minutes. (5) 

 (i) Find the probability that all the custom officers are idle. 

 (ii) Find the expected number of passengers in the queues. 

 (iii) Find the expected waiting time of passenger in the system.