Problems 1

Problem 1 A garment manufacturer has production line making two styles of shirts. Style 1 require 200 grams of cotton thread, 300 grams of dacron thread, and 300 grams of liner thread. Style II require 200 grams of cotton thread, 200 grams of dacron thread and 100 gram of liner thread. The manufacturer make the net profit of Rs. 19.50 on Style I ,Rs. 15.90 on Style II. He has in hand inventory of 24kg. Of cotton thread ,26kg of dacron thread, and 22 kg of liner thread. His immediate problem is to determine the production schedule given the current inventory to make a maximum profit. Formulate the LPP Model Problem 1.2 A firm makes two types of furniture: Chairs and tables. The contribution of each product as calculated by accounting department is Rs. 20 Per chair and Rs 30 per table. Both products are processed on three machines M1,M2 and M3.The time required by each product and total time available per week on each machine are as follow: Machine Chair Table Available Hours M1 3 3 36 M2 5 2 50 M3 2 6 60 How should the manufacturer decides his production in order to maximize contribution?

Problem 1.3 The ABC manufacturing company can make two products p1 and p2.Each of the product requires time on a cutting machine and a finishing machine. Relevant data are: P1 2

P2 1

Cutting Hours(Per Unit) Finishing 3 3 Hours(Per Unit) Profit (Rs. Per unit) 6 4 Maximum 150 200 Sales(Unit Per Week) The number of cutting hours available per week is 390 and number of finishing hours available per week is 810.How much should be produced of each product in order to achieve the profit for the company?

Problem 1.4 A company make two kinds of leather belts. Belt A is a high quality belt, and belt B is of low quality. The respective profits are re.0.40 and re.30 per belt. Each belt of type A requires twice as much time as a belt of type B, and if all belts were of type B, the company could make 1000 per day. The supply of leather is sufficient for only 800 belts per day (both A & B combined). But Belt A requires a fancy buckle & only 400 per day are available. T here are only 700 buckles a day available for belt B. What should be the daily production of each type of belt? Formulate the LPP.

Problem 1.5 Mr. Jain the marketing manager of ABC typewriter company is trying to decide how to allocate his salesman to the company’s three primary markets. Market-1 is an urban area, Market-II is semi-urban area, Market-III is rural area and the salesman can sell on an average 36 and 25 typewriter per week, respectively. For the coming week one of the salesman will be on vacation, leaving only12 men available for duty. Also because of lack of company’s cars, maximum of 5 salesman can be allocated to market area –1.the selling expenses per week per salesman in each area are Rs. 800 per week for area 1.Rs. 700 per week for area –2 , Rs.500 per week for area 3 .The budget for the next week is Rs. 7500.The profit margin per typewriter is Rs.150. Formulate an LPP model to determine how many salesman assign to each area in order to maximise profits Problem 1.6 An animal feed company must produce 200kg of a mixture consisting of ingredients x1 and x2 daily.x1 cost Rs. 3 per kg. And x2 cost Rs. 8 per kg. No more then 80 kgs. Of x1 can be used and atleast 60 kgs. Of x2 must be used.Find out how much of each ingredient should be used if company wants to minimise cost. Problem 1.7 The ABC printing company is facing a tight financial squeeze and is attempting to cut cost wherever possible.At present it has only one one printing contract and luckily the book is selling well in both the backcover and paperback editions.It has just received a request to print more copies of this book in either the handcover or paperback form.Printing cost for hardcover book is Rs.600 per 100 while printing cost for paperback is only Rs.500 per 100.tlhough the company is attempting to economise, it does not wish to lay off any employee.Therefore , it feels obliged to run its two printing presses atleat 80 and 60 hours per week respectively.Press 1 can produce 100 headcover in 2 hour or 100 paperback books in 1 hours Press II can produce 100 headcover in 1 hour or 100 paperback books in 2 hours.Determine how many books of each type should be printed in order to minimise cost. What should be the daily producton of each type of belt? Formulate the LPP. Problem 1.8 A medical scientist claims to have found a cure for the common cold that consists three drugs called K S & H.his results indicate that the minimum daily adult dosage for effective treatment is 10 mg. Of drug K 6mg of durg S, and 8mg. Of drug H. two substances are readily available for preparing pills or drugs each unit of substance A contains 6mg. , 1mg, and 2mg, of drugs of K, S and H respectively and each unit of substance B contains 2mg, 3mg., and 2mg., of the same drugs. Substance A costs rs. 3 per unit and substance B costs rs 5 per unit.

Find the least cost of the combination of two substance s that will give a pill designed two contain the minimum daily recommended adult doses. Problem 1.9. A publisher of text books is in the process of presenting a new book to the market.the book may be bound by either cloth or hard paper. Each cloth bound book sole contributes rs 24, and each paper bound book contributes RS. 23 it takes 10min to bind the cloth cover, and 9mins. to bind the paper back.The total available time for binding is 800 hrs.After considerable market survey it is predicted that the cloth cover sales will exceed at least 10000 copies but the paperâack sales will not be more than 6000 copies . Formulate the problem as a LPP.