Question

Mary Itzoff is a scholarship soccer player at Local University. During the summer she works at a youth all-sport camp that several of the university’s coaches operate. The sports camp runs for eight weeks during July & August. Campers come for a one-week period, during which time they live in the university’s dormitories and use the athletic fields and facilities. At the end of a week a new group of players/campers comes in.

Mary serves primarily 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 campers strip their beds and place their sheets in large bin. Mary must arrange either to purchase new sheets or clean old sheets. A set of new sheets costs $10.00. A local laundry has indicated it will clean a set of sheets for $4.00. Also a couple of Mary’s friends have asked her to let them clean some of the sheets. They have told her they will only charge $2.00 for each set of sheets. However, 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 school and plan to launder the sheets at night in a neighbourhood laundromat.

The following number of campers have registered during each of the eight weeks will operate

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

Based on the discussions with camp administrators from previous summers and on some old camp records and receipts, Mary estimates that about 20% of the cleaned sheets that are returned will have to be discarded and replaced. The campers spill food and drinks on the sheets, and sometimes the stains will not come out of the sheets during cleaning. Also, the campers occasionally tear the sheets or the sheets can be torn at the cleaners. In either case, when sheets come back from the cleaners and are put on the beds, 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 Local University is operations management, and she wants to develop a plan for purchasing and cleaning sheets using linear programming. Help Mary formulate a linear programming model for the problem, and solve it using Excel.

Answer 1