Simplex Method

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A timber merchant manufactures three types of plywood. The data given in the following table shows the production hours per unit in each of three production operations, maximum time available and profits per unit. Operations (hrs) Plywood / II III Profit per unit (Rs) Grade A 2 2 4 40 Grade B 5 5 2 30 Grade C 10 3 2 20 Max time available 900 400 600 How many units of each grade of plywood should be produced to maximise the total profit? 31. A local travel agent is planning a charter trip to a major sea resort. The eight day seven night package includes the fare for the round trip travel, surface transportation, board and lodging and selected tour options. The charter trip is restricted to 200 persons and past experience indicates that there will be no problem in getting 200 persons. The problem for the travel agent is to determine the number of Deluxe, Standard and Economy tour packages to offer for this charter. These three plans each differ according to seating and service on the flight, quality of accommodation, meal plans and tour options. The following table summarises the estimated price for the three packages and the corresponding expenses for the travel agent per person. The travel agent has hired an aircraft for a flat fee of Rs 200000 for the entire trip. Tour plan Price (Rs) Hotel costs (Rs) Meals and other expenses (Rs) Deluxe 10000 3000 4750 Standard 7000 2200 2500 Economy 6500 1900 2200 In planning the trip the following considerations must be taken into account: (a) At least 10 per cent of the packages must be of the deluxe type. (b) At least 35 per cent but not more than 70 per cent must be of the Standard type. (c) At least 30 per cent must be of the Economy type. (d) The maximum number of Deluxe packages available in any aircraft is restricted to 60. (e) The hotel desires that at least 120 tourists should be on the Deluxe and Standard packages together. Determine the number of packages to offer in each type so as to maximise profits.
34. 32. XYZ Company Y\as three departments—assembly, painting and packing, and Can make three types of almirahs. An almirah of Type 1 requires one hour assembly, 40 minutes of painting and 20 minutes of packing time, respectively Similarly almirah of Type II 80 minutes, 20 minutes and 1 hour, respectively. The Type III requires 40 minutes each of assembly, painting and packing time .The total time available at assembly, painting and packing departments is 600 hours, 400 hours and 800 hours, respectively. Type I, Type II and Type III almirahs yield Rs 1000, 1500 and 2000 as profit respectively. (a) Determine the number of almirahs of each type that should be produced in order to maximise the profits. (b) If XYZ Company decides to rent out its capacity to another almirah manufacturer—ABC Company, what should it charge as rental rates? A company makes three products X, Y and Z, which flow through three departments: Drill, Lathe and Assembly. The hours required by each product in each department, the profit contribution of the products and the total time available in each department are shown in the table below: Time required per unit Product Drill Lathe Assembly Profit per unit X 3 3 8 9 Y 6 5 10 15 Z 7 4 12 20 Hours available 210 240 260 35. The marketing department indicates that the sales potential for Products X and Y is unlimited but for the Product Z it is only 30 units. Determine the optimal j product mix. A manufacturer produces four products, A, B, C and D, each of which is processed on three machines, X, Y and Z. The time required for manufacturing one unit of each of the four products and capacity of each machine is indicated as follows:
Page 1 and 2: CONCEPT QUIZ State True or False. 1
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