OPERATIONS RESEARCH ASSIGNMENT-1

COMMON FOR BOTH CSE-A&B

OPERATIONS RESEARCH(IV/IV CSE A&B , SEM – I)

ASSIGNMENT – I

1.     A company produces two types of leather belts A and B . A is of superior quality and B is of inferior quality . The respective profits are Rs. 10 and Rs. 5 per belt . The supply of raw material is sufficient for making 850 belts per day . For belt A , a special type of buckle is required and 500 are available per day . There are 700 buckles available for belt B per day . Belt  A needs twice as much time as that required for belt B and the company can produce 500 belts if all of them were of the type A . Formulate a LP model for the above problem .

2.     The standard weight of a special purpose brick is 5 kg. and it contains two ingredients B1 and B2 , B1 costs Rs. 5 per kg. and B2 costs Rs. 8 per kg. Strength considerations dictate that the brick contains not more than 4 kg. of B1 and a minimum 2 kg. of B2 since the demand for the product is likely to be related to the price of the brick . Formulate the above problem as a LP model .

3.     Egg contains 6 units of vitamin A per gram and 7 units of vitamin B per gram and cost 12 paise per gram .Milk contains 8 units of vitamin A per gram and 12 units of vitamin B per gram and costs 20 paise per gram . The daily minimum requirement of vitamin A and vitamin B are 100 units and 120 units respectively . Find the optimal product mix .

4.     In a chemical industry two products A and B are made involving two operations . The production of B also results in a by-product C . The product A can be sold at Rs. 3 profit per unit and B at Rs. 8 profit per unit . The by-product C has a profit of Rs. 2 per unit but it cannot be sold as the destruction cost is Re. 1 per unit . Forecasts show that upto 5 units of C can be sold . The company gets 3 units of C for each units of A and B produced . Forecasts show that they can sell all the units of A and B produced . The manufacturing times are 3 hours per unit for A on operation one and two respectively and 4 hours and 5 hours per unit for B on operation one and two respectively . Because the product C results from producing B , no time is used in producing C . The available times are 18 and 21 hours of operation on one and two respectively . How much of A and B need to be produced keeping C in mind , to make the highest profit . Formulate the above problem as LP model .

5.     A company produces two types of hats . Each hat of the first type requires as much labour time as the second type . If all hats are of the second type only , the company can produce a total of 500 hats a day . The market limits daily sales of the first and second type to 150 and 250 hats . Assuming that the profits per hat are Rs. 8 for type B , formulate the problem as a linear programming model in order to determine the number of hats to be produced of each type as to maximize the profit .

6.     A company desires to devote the excess capacity of the three machines lathe , shaping machine and milling machine to make the products A , B and C . The available time per month in these machinery are tabulated below :

Machine	Lathe	Shaping	Milling
Available time/month	200 hrs	100 hrs	180 hrs

The time taken to produce each unit of the products A , B and C on the machines is displayed in the table below :

	Lathe	Shaping	Milling
Product A hrs	6	2	4
Product B hrs	2	2	--
Product C hrs	3	--	3

The profit per product would be Rs. 20 , Rs. 16 and Rs. 12 respectively on the product A , B and C .

Formulate a LPP to find the optimum product mix .

7.     An animal food company must produce 200 kg. of a mixture consisting of ingredients x1 and x2 daily . x1 costs Rs. 3 per kg. and x2 Rs. 8 per kg. No more than 80 kg. of x1 can be used and at least 60 kg. of x2 must be used . Formulate a LP model to minimize the cost .

8.     A small manufacturer employs 5 skilled men and 10 semi-skilled men for making a product in two qualities : a deluxe model and an ordinary model . The production of a deluxe model requires 2-hour work by a skilled man and a 1-hour work by a semi-skilled man . The ordinary model requires 2-hour work by a skilled man and 3-hour work by a semi-skilled man . According to workers union rules , no man can work more than 8 hours per day . The profit of the deluxe model is Rs. 1000 per unit and that of ordinary model is Rs. 800 per unit . Formulate a LP model for this manufacturing situation to determine the production volume of each model such that the total profit is maximized .

  LAST DATE FOR SUBMISSION : 10-JULY-2012

ANITS CSE(2009-13)!!!