Formulation

Here you will find problems and solutions related to Formulation.

(Q) A manufacturer of lether belts makes three types of belts A, B and C which are processed on three machines M1 M2 and M3 Belt A requires 2 hours on machine M1 and 3 hours on machine M3 Belt B requires 3 hours on machine M1 2 hours on machine M2 and 2 hours on machine M3 and Belt C requires 5 hours on machine M2 and 4 hours on machine M3.There are 8 hours of time per day available on machine M_{1} 10 hours time per day available on machine M2 and 15 hours of time per day available on machine M3.The profit per unit of A, B and Care Rs. 3.00, Rs. 5.00 and Rs. 4.00 respectively. Find out the daily production of each type of belts such that the profit be maximum.

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(Q)A firm can produce three types of cloth say A, B and C. Three kinds of wool are required for it, say red wool, green wool and blue wool. One unit length of type A cloth needs 2 yards of red wool and 3 yards of blue wool; one unit length of type B cloth needs 3 yards of red wool, 2 yards of green wool and 2 yards of blue wool; and one unit length of type C cloth needs 5 yards of green wool and 4 yards of blue wool. The firm has only a stock of 8 yards of red wool, 10 yards of green wool and 15 yards of blue wool. It is assumed that the income obtained from one unit length of type A cloth is Rs. 3.00, of type B cloth is Rs. 5.00 and that of type C cloth is Rs. 4.00. Formulate the above problem as a linear programming problem.

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(Q)A manufacturer of furniture makes two products, chairs and tables. Processing of these products is done on two machines A and B. A chairs requires 2 hours on machine A and 6 hours on machine B. A table requires 5 hours on machine A and no time on machine B. There are 16 hours of time per day available on machine A and 20 hours on machine B. Profit gained by the manufacturer from a chair and table is Rs. 10 and Rs. 50 respectively. What should be the daily production of each of the two products to obtain maximum profit? (Formulate the problem).

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(Q) A particular company manufactures two products A and B. These products are processed on the same machine. It takes 25 minutes to process one unit of product A and 15 minutes for one unit of product B and the machine operates for a maximum of 35 hours in a week. Product A requires 1 kg. and product B. 2.5 kg. of raw-material per unit, the supply of which is 170 kgs per week. If the net profit from the product are Rs. 100 and Rs. 450 per unit respectively, find how much of each product should be produced per week, in order to get maximum profit. (Formulate it mathematically).

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(Q) A person requires 10, 12 and 12 units of chemical A, B and C respectively for his garden. A liquid product contains 3, 2 and 1 unit of A, B and C respectively per jar. A dry product contains 1, 2 and 4 units of A, B and C per packet. If the liquid product sells for Rs. 3.00 per jar and the dry product sells for Rs. 2 per packet then formulate the problem as a linear programming problem.

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(Q) Food X contains 6 units of vitamin A per gram and 7 units of vitamin E per gram and cost 12 paise per gram. Food Y contains 8 units of vitamin A per gram and 12 units of vitamin B and cost 20 paise per gram. The daily minimum requirement of vitamin A and B are 100 units and 120 units respectively. Find the minimum cost of product mix. (Formulate the problem).

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(Q) A television company has three major departments for the manufacture of two models, A and B. Monthly capacities are given as follows.

The marginal profit of model A is Rs.400 each and and that of model B is Rs. 100 each.Assuming that the company can sell any quantity of eighter product due to favourable market conditions, determine the highest possible profit for this month. (Formulate it).

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(Q) A company sells two different products A and B. The company makes a profe of Rs. 40 and Rs. 30 per unit of products A and B respectively. The two products are produced in a common production process and are sold in two different markets. The production process has a capacity of 30,000 man houn It takes 3 hours to produce one unit of A and one hour to produce one unit of B. The market has been surveyed and the company officials feel that the maximum number of unit of A that can be sold is 8,000 and the maximum of B is 12,000 units. Subject to these limitations, formulate the problem as a LPP.

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(Q) A furniture manufacturer wishes to determine the number of tables and chairs to be made by him in order to optimise the use of his available resources. These products utilize two different types of timber and he has in hand 1,500 board feet of the first type and 1,000 board feet of the second type. He has 800 mas hours available for the total job. Each table and chair requires 5 and 1 board feet respectively of the first type timber and 2 and 3 board feet of the second type. 3 man hours are required to make a table and 2 man hours are needed to make a chair. The manufacturer makes a profit of Rs. 12 on a table and Rs. 5 on a chair. Write down the complete linear programming formulation of the problem in terms of maximising the profit.

(Q) A tailor has 80 sq m of cotton material and 120 sq m of woollen material A suit requires 1 sq m of cotton and 3 sq m of woollen material and a dress requires 2 sq m of each. A suit sells for Rs. 500 and a dress sells for Pls. 400 Pose & L.P.P. in terms of maximizing the income.

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(Q) A farmer has a 100 acre farm. He can sell all tomatoes, lettuce or radishes he can raise. The price he can obtain is Rs. 1.00 per kg. for tomatoes Rs. 0.75 & head for lettuce and Rs. 2.00 per kg for radishes. The average yield per acre is 2,000 kgs of tomatoes, 3,000 heads of lettuce and 1,000 kgs of radishes Fertilizer is available at Rs. 0.50 per kg and the amount per acre is 100 kgs each for tomatoes and lettuce and 50 kgs for radishes. Labour required for sowing, cultivating and harvesting per acre is 5 man days for tomatoes and radishes and 6 man-days for lettuce. A total of 400 man-days of labour are available at Rs. 20.00 per man-day. Formulate this problem as a linear programming model to maximize the total profit.

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(Q) A manufacturer makes red and blue pen. A red pen takes twice as much as time to make a blue pen one. If the manufacturer makes only blue pens, 500 can be made in a day. A red pen sells for Rs. 8 and at most 150 can be sold in a day. A blue pen sells for Rs. 5 and at most 250 can be sold in a day. The manufacturer desires to maximize

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(Q) At a cattle breeding firm, it is prescribed that the food ration for one animal must contain at least 14, 22 and 11 units of nutrients A, B and C respectively. Two different kinds of fodder are available. Each unit weight of these two contains the following amounts of the three nutrients.

It is given that the cost of fooder 1 and 2 are 3 and 2 monetary units respectively. Formulate the problem of finding the minimum cost of purchasing the folders as L.P.P.

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(Q)A medicine firm manufacturing two types of medicines A and B, can make a profit of Rs. 20 per bottle of A and Rs. 30 per bottle of B. Both A and B need for their production two essential chemicals Cand D. Each bottle of A requires 3 litres of C sad 2 litres of D and each bottle of B requires 2 litres of C and 4 litres of D. The total supply of these chemicals are restricted to 210 Litres of C and 300 litres of D. Type B medicine contains alcohol and so its manufacture la restricted to 65 bottles per day. Construct a linear programming proble in terms of maximizing the daily profit of the product.

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(Q)A manufacturer of furniture makes two producte, chairs and tables. Processing of the producte la dous on two machione A and D. A chair requires 2 hours an machine A and 6 hours on machine 13. A table requires 5 hours on machine A and 2 hours on machine D. There are 16 hours of time per day available on machine A and 22 hours on machine D. Profit gained by the manufacturer from a chair and a table is Re. 1 and Rs. 5 respectively. Formulate a linear programming problem to maximise proft per day.

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