A company needs to order raw material and demand is forecast to be normally distributed with a mean of 250 gallons and standard deviation of 100 gallons. One gallon of raw material produces one gallon of product and the product sells for $25/gallon. Raw material costs $10/gallon but the company must also spend $5/gallon for disposal of any UNUSED raw material. If demand is higher than production capacity, the company sells what it can make and loses the rest of demand. a) If they buy 400 gallons of raw material, how much should they expect to spend on disposal costs (in $)? b) To have a 92% probability of satisfying demand, how many gallons of raw material should be bought?

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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A company needs to order raw material and demand is forecast to be normally distributed with a mean of 250 gallons and standard deviation of 100 gallons. One gallon of raw material produces one gallon of product and the product sells for $25/gallon. Raw material costs $10/gallon but the company must also spend $5/gallon for disposal of any UNUSED raw material. If demand is higher than production capacity, the company sells what it can make and loses the rest of demand. a) If they buy 400 gallons of raw material, how much should they expect to spend on disposal costs (in $)? b) To have a 92% probability of satisfying demand, how many gallons of raw material should be bought?
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