T-time makes and sells 16oz bottles of freshly brewed iced tea from small display stands in upscale grocery stores the Houston area. All tea is made early in the morning and delivered to the grocery stores around 7:00am. The total cost of making each bottle of tea is $1.25 and the glass bottle itself costs $.35.
A bottle of tea retails for $2.75. Demand can vary from 500 to 3,500 any day and is following a uniform distribution. At the end of each day (8:00pm) all remaining inventory is emptied into a large container and delivered to a retirement home for the symbolic price of $.05/oz.
After the bottles are emptied, they are cleaned and can then be reused the following day. The cost of cleaning a bottle is $.10 and restocking an empty bottle is an additional $.05.
a) What is the optimal number of bottles iced tea to make each morning?
b) What is the average daily revenue from tea sold to the retirement home?
c) What is the expected daily cleaning cost?
d)What is the expected daily stock-out cost?
e) Suppose the purchasing cost could be lowered by $.30/bottle. How would this affect your answer above? Be specific.