Milk is stocked at the grocery store each week. At the end of the week unsold milk is reduced in price by 70% and always sells for this lower price instantly
If weekly demand for milk is normally distributed with a mean of 200 gallons and standard deviation of 25 gallons, find the price for which a fresh gallon of milk sells. Assume a service level of 95% and that the store purchases milk for $2 per gallon.
Service level = Cs/(Cs + Co). If the selling price per gallon is X the salvage price is .3X. Thus, Cs = X-2 and Co = 2 - .3X. Solving .95 = X - 2/(X - 2 + 2 - .3X) gives X = $5.97, so the milk sells for $5.97 per gallon.
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