A store is getting ready for Valentine's day and needs to purchase Valentine's day decorations, which will be sold prior to the holiday. The store has not yet found a supplier for the decorations yet, but has done some market research. Based on that research they anticipate a 30% chance that they can get the decorations for $8.50 per box, a 60% chance they can get the decorations for $10 per box, and a 10% chance that they will have to pay $13 per box.

Due to the high demand leading up to Valentine's day, the decorations are sold at $15 per box. However, after the holiday, these decorations will have to be marked down in order to sell them all. It is uncertain what average sales price will ensure that all the leftover decorations are sold. Based on market forecasts, the average sale price that will clear out the leftovers is equally likely to be any price between $6.50 and $13.50 per box.

Demand prior to the holiday is expected to be normally distributed with a mean of 40 boxes and a standard deviation of 10 boxes (round to the nearest integer value).

Please use the following Excel to determine how many decorations the store should pre-purchase to maximize their expected profit?