Problem
Mary sells hats for $11 apiece. However, when the concert ends unsold hats have no value. Due to a licensing agreement, Mary needs to make sure that leftover hats are destroyed using a method that ends up costing $0.25 for each unsold Hat. It costs Mary $7.50 to buy a specialty hat from the supplier. The supplier she uses has a cost per hat of $3. Mary estimates that demand is distributed as shown below.
Demand 325 350 375 400 425 450
Probability 0.10 0.15 0.10 0.20 0.25 0.20
Cum. Prob.
How many specialty hats should Mary buy from the supplier to maximize her profits?