Mom and Pop have decided to open a grocery store. Mom and Pop buy tomatoes every

Question

Mom and Pop have decided to open a grocery store. Mom and Pop buy tomatoes every day to ensure fresh produce. Each morning any tomatoes that are left over from the previous day are sold to a nearby restaurant that can use the tomatoes in their soups. Mom and Pop can buy tomatoes from their supplier for $3 per lb. The tomatoes are sold to store customers for $5.5 per pound and the restaurant is willing to pay $1 per pound. You can assume that the demand follows a uniform distribution ~ U(15, 35) pounds per day.

How many pounds of tomatoes should you purchase?

Select one: a. 5 b. 15 c. 11 d. 26 e. 46

Explanation / Answer

The problem will be solved using Newsvendor model.

Given:

Purchase price of tomato = C = $3/lb

Sell price price of tomato = S = $ 5.5 / lb

Salvage price restaurant is willing to pay = S = $1

Thus, Underage cost = Cu = $5.5 - $3 = $2.5

Overage cost = Co = $ 3 - $ 1 = $2

Therefore , Critical ratio = Cu/ Cu + Co = 2.5 / ( 2.5 + 2 ) = 2.5/4.5 = 0.5555

Critical ratio is the probability of the optimuM quantity to be ordered.

Thus probability = 0.5555

Corresponding quantity to be ordered with demand having uniform distribution

= 15 + ( 35 - 15) x 0.5555

= 15 + 11.11

= 26.11 ( 26 rounded to nearest whole number )

ONE SHOULD PURCHASE 26 POUNDS OF TOMATO

Underage cost = Cu =

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