Problem
The Halloween season is approaching, and Scarybooh (a local sustainable party props store) is preparing to receive customer orders from all over the country. One of Scarybooh's best-sellers is pumpkins it buys from a nearby farm. Each pumpkin takes 90 days to mature after seeds are planted, so they should be ordered with enough time in advance. The store manager, Kelly Torres, should place the pumpkins order today to guarantee they'll arrive on time for the upcoming season. She should be careful with her calculations considering that if additional pumpkins are ordered close to Halloween, those will not arrive on time. Each pumpkin costs $11 and is sold for $30. Based on historical data, the pumpkin season demand is normally distributed with a mean of 1500 units and a standard deviation of 296.
A. Based on the available information, what's the critical ratio for this product?
B. How many units of pumpkins should Scarybooh order to maximize the expected profit for this Halloween season?
C. If Kelly orders the number of units calculated in Question A, what would be Scaryboo's expected profit?
D. After further analysis, Kelly suggests selling the pumpkins at a discounted price of $8 on the last day of the season. What is the new order quantity that would maximize the expected profit for this product?
E. The warehouse manager Mr. Bell tells Kelly that they cannot order more than 1000 pumpkins, considering there is a limited storage capacity and they need space for many other Halloween decorations. If Kelly orders 1000 pumpkins, what would be the expected units short during this season?