Ahotel 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, cost of a fast one day laundry service is 40 cents per towel and the cost of a slow two day laundry service is 25 cents 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 rental service have washed by different laundry services so as to minimize total costs?

The hotel rental service needs to buy 400 new towels, have 400 towels washed by fast one day laundry service and 100 towels washed by slow two day laundry service in order to minimize total cost.

Step-by-step explanation:

The hotel rental service needs 300 towels on the first day. Since this is the first day, they would need to buy 300 new towels costing $300. By the second day, they would be needing only 200 clean towels. Hence, to cut cost, instead of having all 300 dirty towels from the first day washed by the fast one day laundry service which would have amounted to $120, they should have the fast one day laundry service wash only 200 giving $80 and give the remaining 100 to the slow 2 days laundry service at the cost of $25. This means they would have spent a total of $105 instead of $120 in getting the 300 towels clean.

On the third day, a total of 400 clean towels are required. Since we already have 100 towels ready from the first day,more 300 towels are needed. To save cost, the hotel has to do a fast one day laundry service on the 200 towels used on the second day and buy more 100 new towels. This will certainly cut cost than purchasing 300 new towels.

Hence, the hotel rental service needs to buy a total of 400 new towels, the fast one day laundry service needs to wash a total of 400 towels while the slow two days laundry service will need to wash 100 towels in order to minimize total cost.