Milk is stocked at the grocery store each week. At the end of the week unsold mi
ID: 375707 • Letter: M
Question
Milk is stocked at the grocery store each week. At the end of the week unsold milk is reduced in price by 60% and always sells for this lower price instantly. If weekly demand for milk is normally distributed with a mean of 300 gallons and standard deviation of 45 gallons, find the price for which a fresh gallon of milk sells. Assume a service level of 97.5% and that the store purchases milk for $2.44 per gallon. (Show all work)
(This question was answered wrong on chegg so posting again for right answer!)
Explanation / Answer
This is a newsvendor type problem where Service level ( in fractional terms ) = Critical ratio
Critical ratio = Cu / Cu + Co
Cu = Cost of underage = Price / unit – Purchase cost/ unit = $ P - $2.44 ( Assume purchase price = $ P / Gallon)
Co = Cost of overage = Purchase cost / unit – Salvage price/ unit = $2.44 - $0.4.P ( remarks : since milk price is discounted by 60%, salvage price will be 40% original selling price )
Hence
Critical Ratio = Cu/ Cu + Co = ( P – 2.44) / ( P – 2.44 + 2.44 – 0.4P) = ( P – 2.44) / 0.6.P
Since Service level ( in fraction terms = 0.975 = Critical ratio
Hence,
0.975 = ( P – 2.44)/0.6.P
Or, 0.6 x 0.975.P = P – 2.44
Or, 0.585.P = P – 2.44
Or, 0.415.P = 2.44
Or, P = 5.88 ( rounded to 2 decimal places )
PRICE FOR WHICH A FRESH GALLON OF MILK SELLS = 5.88
PRICE FOR WHICH A FRESH GALLON OF MILK SELLS = 5.88