Quantitative questions

1. Simon School Volunteers decide to bake pies for a bake sale organized to raise money for Habitat for Humanity. The volunteers calculate that the cost of ingredients for each pie will be approximately $3.00. The volunteers further estimate that if they price the pies at $10 a piece they will sell between 37 and 42 pies (any number between 37 and 42 is equally likely). The rules of the bake sale are such that prices may not be adjusted in the middle of the sale. Unsold pies will be delivered to a food pantry.
   1. For Simon School Volunteers, what is the cost of overprovisioning (C_o), i.e.baking a pie that does not sell?
   2. For Simon School Volunteers, what is the cost of underprovisioning (C_u), i.e. per-pie profit that they miss out on when they do not have enough pies to satisfy the demand?
   3. What is the value of the critical ratio (C_u/(C_u+C_o))?
   4. If the volunteers decided to sell the pies for $10 a piece, how many pies should they bake to maximize their expected (i.e. mean) profits from the sale? You may find the plot below useful in answering this question.

Quantile Plot -- Demand Distribution @ $10 per pie 43 42 41 40 3.9 37 36 20% 30%% 40% 50% 70% BOM 100%%Inverse Cumulative Probability Distribution of Demand 45 44 43 42 41 40 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%