Everyone is perplexed that Katelyn just bought a crazy amount of laundry detergent. Katelyn lives with 3 roommates who share laundry facilities. Katelyn found an online detergent company that offers a price discount, so she set up a quantity discount table like she learned about in college. All the roommates share the same detergent and the house goes through 1 bottle every two months or 6 per year. Katelyn estimated $5 to place an order. She also estimated that the holding cost would be about 4%, the interest on the money tied up in inventory. The laundry company says they charge $4 per bottle for orders of up to 49. They charge $3.75 for orders between 50 and 99. If an order is 100 or more they charge only $3.50 per bottle.

1. first make a table to determine the optimal number of bottles to order at a time, given her estimates.

2. How many bottles did Katelyn order, if she used the optimal from this model?

3. If Katelyn ordered that amount, how many years worth of detergent would it be?

4. Katelyn set up her table correctly, but the amount she ordered seems unrealistic. Why?