A bakery would like you to recommend how many loaves of its famous marble rye br

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 $7.00. 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 are 30%, 25%, and 45% respectively.

a. find the expected monetary value when baking 25 loaves.

b.find the expected monetary value when baking 50 loaves.

c. find the expected monetary value when baking 75 loaves.

d. make a recommendation for the bakery to bake 25, 50 or 75 loaves each morning based on the above responses.

Explanation / Answer

Expected monetary gain = expected revenue - cost

a. expected monetary value when baking 25 loaves = 25*($7) * (Probability of having demand at least 25) - 25*4

= 25*7*1- 25*4 = $75

b. expected monetary value when baking 50 loaves:

Expected revnue = 25*0.30*7 + 50*0.70*7 = 297.5

Cost = 50*4 = 200

expected monetary value when baking 50 loaves = 297.5-200 = $97.5

c. expected monetary value when baking 75 loaves:

Expected revnue = 25*0.30*7 + 50*0.25*7+ 75*0.45*7 = 376.25

Cost = 75*4 = 300

expected monetary value when baking 50 loaves = 376.25-300 = $76.25

d. Since expected monetary values from baking 25, 50 and 75 loaves are $75, $97.5 and $76.25 respectively, it is recommended that bakery should bake 50 loaves

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