1. A 24-hour supermarket has the following minimal requirements for cashiers:
Period| 1| 2| 3| 4| 5| 6|
Time of day(24 hr)| 3-7| 7-11| 11-15| 15-19| 19-23| 23-03| Min.# reqd.| 7| 20| 14| 20| 10| 5|
Period 1 follows immediately after period 6. A Cashier works eight consecutive hours, starting at the beginning of one of the six time periods. Determine a daily employee worksheet which satisfies the requirements with the least number of personnel. Formulate the problem as a LPP.
2. An agriculturist has a 125-acre of farm. He produces radish(Gajar), peas (Mutter) and potato (Alu). Whatever he raises is sold fully in the market. He gets Rs 5 per kg of radish. Rs 4 per kg of mutter and Rs. 5 per kg for potato. The average yield per acre is 1500kg of radish, 1800 kg of mutter and 1200 kg of potato. To produce each 100 kg of radish and mutter, and 80 kg of potato, a sum of Rs. 12.50 has to be used for fertilizers. Labour required for each acre to raise the crop is 6 man-days for radish and potato each; and 5 man days for mutter. A total of 500 man-days of labour at a rate of Rs. 40 per man-day is available. Formulate this as a LPP to maximize the profit of the agriculturist.
3. The Marketing department of Everest Company has collected information on the problem of advertising for its products. This relates to the advertising media available, the number families expected to be reached with each alternative, cost per advertisement, the maximum availability of each medium and the expected exposure of each one (measured as the relative value of one advertisement in each of the media): The information is given below: Media| No. of families expected to cover| Cost per ad (Rs.)| Max availability (No. of times)| Expected exposure (units)| TV (30sec)| 3000| 8000| 8| 80|
Radio (15sec)| 7000| 3000| 30| 20|
Sunday Ed. Of a Daily(1/4page)| 5000| 4000| 4| 50|
Magazine (1page)| 2000|...