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Formulation of lp problems

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Formulation of lp problems

1. 1. ASSIGNMENT- 3 LP - FORMULATION #1 A local travel agent is planning a charter trip to a major sea resort. The eight days /seven nights package includes the fare for round trip travel, surface transportation boarding and lodging and selected tour options. The charter trip is restricted to 200 persons and past experience indicates that there will not be any problem for getting 200 persons. The problem for the travel agent is to determine the number of Deluxe, standard and Economy tour packages to offer by this charter. These three plans differ according to seating and service for the flight, quality of accommodations, meal plans and tour options. The following table summarizes the estimated prices for the three packages and corresponding expenses for the travel agent. The travel agent has hired an aircraft for the flat fee of Rs200,000 for the entire trip. Tour PlanPrices and costs for tour packages per person Price(Rs.) Hotel cost(Rs.) Meal and other expenses Deluxe 10,000 3,000 4,750 Standard 7,000 2,200 2,500 Economy 6,500 1,900 2,200 In planning the trip, the following consideration must be taken in to account: i. At least 10% of the packages must be Deluxe type. ii. At least 35% but not more than 70% of Standard Type. iii. At least 30% must be of the Economy type. iv. The maximum number of Deluxe packages available in any aircraft is restricted to 60. v. The hotel desires that at least 120 of the tourists should be on the Deluxe and Standard packages together. The travel agent wishes to determine the number of packages to offer in each type so as to maximize the total profit. Maximize Z = Rs[x1(10,000-3000-4750) + x2(7000-2200-2500) + x3(6500-1900-2200)-200000] = Rs(2250x1 +2300x2+ 2400x3 – 200000) Subject to: #2
2. 2. M & M Breweries Ltd. has two bottling plants, one located at Karachi and the other at Kotri. Each plant produces three drinks, soda, fruit juice and cola drink named A, B and C respectively. The number of bottles produced per day are as follows: Plant at Karachi Kotri Soda (A) 1500 1500 Fruit juice (B) 3000 1000 Cola drink (C) 2000 5000 A market survey indicates that during the month of April, there will be a demand of 20,000 bottles of soda, 30,000 bottles of fruit juice and 50,,000 of cola drink. The operating cost per day for plants at Karachi and Kotriare 600 and 400 monetary units. For how many days each plant be run in the month of April so as to minimize the operating cost, while meeting the market demand? #3 A firm manufactures three products A, B and C. Time to manufacture product Ais twice that for B and thrice that for C and if the entire labor is engaged in making product A 1600 units of this product can be produced. These products are to be produced in the ratio of 3:4:5. The relevant data is given below. There is demand for at least 300, 250 and 200 units of product A, B and C and the profit earned per unit is Rs. 90, Rs.40 and Rs. 30 respectively. Formulate a LP problem. Raw material Requirement per unit of product Total availability (kg) (kg) A B C P 6 5 2 5000 Q 4 7 3 6000 Formulation of L.P Model. Let x1,x2 , andx3 denote the number of units of product A ,B and C to be manufactured. The objective is to maximize Z = 90x1 + 40x2 + 30x3, Subject to: 6x1 + 5x2 + 2x3 4x1 + 7x2 + 3x3 The product B requires one half and C requires one third the time required for product A. let time t is required to produce one unit of A. Hence 1600t is the time required to produce 1600 units of A. Therefore the constraint is or Market demand requires Finally, since products A,B and C are to be produced in the ratio of 3:4:5, , Thus there are two additional constraints