A baker bakes fresh apple pies at the beginning of everyday. At the end of the d

Question

A baker bakes fresh apple pies at the beginning of everyday. At the end of the day, unsold pies are reduced in price by 70% and always sell out for this lower price instantly (discounted products are sold at a loss). If demand for pies is normal with a mean of 200 pies and standard deviation of 25 pies, find the price a fresh pie sells for. Assume a service level of 95% and that the baker purchases ingredients for $2 per pie (assume labour cost is zero).
Round your final answer only. Round your final answer to 2 decimal places.

The average daily demand of a bottle of paint thinner at a hardware store has a standard deviation of 5 units. If lead time is 2 days, and re-order point with 90% service value is 39, what is the average daily demand?

Round all your numbers except your final answer to 2 decimal places. Round your final answer to the nearest integer.

Explanation / Answer

Let the price at which fresh pie sells for = P

Cost of buying ingredient = C =$2 per pie

Salvage value of unsold pie ( discounted by 70% ) = 0.30.P

Cost of underage =Cu = P – C

Cost of overage = CO =C – 0.3.P

Critical ratio = Cu/ Cu + Co = ( P – C ) / ( P – C + C – 0.3.P) = ( P – C ) /0.7P

Critical ratio is the probabilityof optimum order quantity or in stock probability

The ins tock probability here is = 95% = 0.95

Therefore , ( P -C) / 0.7.P = 0.95

Or, P – C = 0.665.P

Or, 0.335.P = C

Or, 0.335 = $2

Or, P = $2/0.335

Or, P = 5.97

PRICE AT WHICH FRESH PIE SELLS AT = $5.97

Z value for 90 % service level = NORMSINV ( 0.90 ) = 1.2815

Standard deviation of average daily demand = 5 units

Lead time = 2 days

Therefore , Standard deviation of average demand during lead time = 5 x Square root ( 2 ) = 5 x 1.414 = 7.07 ( 7 rounded to nearest whole number )

Safety stock = Z value x Standard deviation of average demand during lead time = 1.2815 x 7.07 =9.06

Reorder point = Daily demand x Lead time ( days ) + safety stock

Or, 39 = Average daily demand x 2 + 7

Or, 2 x average daily demand = 32

Or, Average daily demand = 32/2 = 16

AVERAGE DAILY DEMAND = 16 UNITS

PRICE AT WHICH FRESH PIE SELLS AT = $5.97

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