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# Quantitative Methods/Linear Problem - Mary Kelly

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Mary Kelly is a scholarship soccer player at state university. During the summer she works at youth allsports camp that several universitie's coaches operate. the sports camp runs for 8 weeks during July and August. Campers come for one week period, during which time they live in the State dormitories and use the state athlectic fields and facilities. At the end of a week a new group of kids comes in.Mary primarily serves as one of the camp soccer instructors. However, she has also been placed in charge of arranging for sheets for the beds the campers will sleep on in the dormitories. Mary has been instructed to develop a plan for purchasing and cleaning sheets each week of camp at the lowest possible cost.

Clean sheets are needed at the beginning of each week, and the campers use the sheets all week. At the end of the week the campers strip their beds and place the sheets in large bins. Mary must arrange either to purchase new sheets or to clean old sheets. A a set of new sheets cost \$10.00. Alocal laundry has indicated that it will clean a set of sheets for \$4.00. Also, a couple of Mary's friend have asked her to them clean some of the sheets. They have told her they will charge only \$2.00 for each set of sheets they clean. However, while the laundry will provide cleaned sheets in a week, Mary's friends can only deliver cleaned sheets in two weeks. They are going to summer and plan to launder the sheets at night at a neighborhood laundromat.

The accompanying table lists the number of campers that have registered during each of the eight weeks the camp will operate. Based on discussions with camp administrators from previous summers and on some old camp records and receipts, Mary estimates that each week about 20% of the clean sheets that are returned will have to be discarded and replaced. The campers spilled food and drinks on the sheets, and sometimes the stains will not come out during cleaning. Also, the campers occassionally tear the sheets or the sheets can get torn at the cleaners. Either case when the sheets come back from the cleaners and are put on the bed, 20% are taken off and thrown away.

At the beginning of the summer the camp has no sheets available, so initially sheets must be purchased. Sheets are thrown away at the end of the summer.

Mary's major at State is Management Science and she wants to develop a plan for purchasing and cleaning sheets using Linear Programming. Help Mary formulate a Linear Programming Nodel for this problem and solve it using the computer.

Week Registered Campers
1 115
2 210
3 250
4 230
5 260
6 300
7 250
8 190

The problem does not have to be solved can you just formulate the Linear Programming method?