Question

A hotel rental service needs to have clean towels for each day of a three-day period. Some of the clean towels may be purchased new and some may be dirty towels from previous days that have been washed by a laundry service. The cost of new towels is $1 per towel, the cost of a fast one-day laundry serice is 40t per towel, and the cost of a slow two-day laundry service is 254 per towel. If the rental service needs 300, 200, and 400 clean towels for each of the next three days (respectively), how many towels should the rental service buy new and how many should the rental service have washed by the different laundry services so as to minimize total costs?

Let x, y, z, and w be the number of towels purchased new, the number of towels washed by the one-day service after the first day, the number of towels washed by the one-day service after the second day, and the number of towels washed by the two-day service after the first day respectively and let C be the total costs.

Answer 1