Question

A bakery would like you to recommend how many loaves of its famous marble rye bread to bake at the beginning of the day. Each loaf costs the bakery ​$4.00 and can be sold for ​$5.00. Leftover loaves at the end of each day are donated to charity. Research has shown that the probabilities for demands of​ 25, 50, and 75 loaves are 30​%, 25​%, and 45​%, respectively. Make a recommendation for the bakery to bake​ 25, 50, or 75 loaves each morning. Find the expected monetary value when baking 25 loaves. EMVequals​$ nothing ​(Type an integer or a​ decimal.) Find the expected monetary value when baking 50 loaves. EMVequals​$ nothing ​(Type an integer or a​ decimal.) Find the expected monetary value when baking 75 loaves. EMVequals​$ nothing ​(Type an integer or a​ decimal.) Make a recommendation for the bakery to bake​ 25, 50, or 75 loaves each morning. The bakery should bake ▼ 25 50 75 loaves of bread every morning.

Answer 1

When baking 25 loaves -

Profit = $5 - $4 = $1 for 25 loaves irrespective of the demand of 25, 50, or 75.

EMV = $1 * 25 = $25

When baking 50 loaves -

Profit = $1 for 25 loaves and -$4 for leftover 25 loves when the demand of 25 (p = 0.3)

=> Profit = -$75 for p = 0.3

Profit = $5 - $4 = $1 for 50 loaves for the demand of 50 or 75 (p = 0.25 + 0.45 = 0.7)

EMV = -$75 * 0.3 + $50 * 0.7  = $12.5

When baking 75 loaves -

Profit = $1 for 25 loaves and -$4 for leftover 50 loves when the demand of 25 (p = 0.3)

=> Profit = -$175 for p = 0.3

Profit = $1 for 50 loaves and -$4 for leftover 25 loves when the demand of 50 (p = 0.25)

=> Profit = -$50 for p = 0.25

Profit = $5 - $4 = $1 for 75 loaves for the demand of 75 (p = 0.45)

EMV = -$175 * 0.3 - $50 * 0.25 + $75 * 0.45 = -$31.25

Since the EMV for baking 25 loaves is maximum,  

The bakery should bake 25 loaves of bread every morning.