Farm Grown, Inc., produces cases of perishable food products. Each case contains

Question

Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any cases not sold by the end of the day, they are sold to a large food processing company for $3 a case. The probability that daily demand will be 100 cases is 0.3, the probability that the demand will be 200 cases is 0.4, and the probability that daily demand will be 300 cases is 0.3.

Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case.

Suppose you have reason to believe the probabilities may not be reliable due to changing conditions. If these probabilities are ignored, what decision would be made using: (a) the optimistic criterion? (b) the pessimistic criterion?

Explanation / Answer

Let daily produce be x cases.

Now, x can be 100, 200 or 300 as demand can be any one of the three.

a. For optimistic criterion, expected demand is 300. Hence 300 cases should be produced

b. For pessimistic criterion, demand is 100. So, 100 cases should be produced

Produced Demand Total profit 100 100 100*(15-5) = 1000 100 200 100*(15-5) + 100*(15-16) = 900 100 300 100*(15-5) + 200*(15-16) = 800 200 100 100*(15-5) + 100*(3-5) = 800 200 200 200*(15-5) = 2000 200 300 200*(15-5) + 100*(15-16) = 1900 300 100 100*(15-5) + 200*(3-5) = 600 300 200 200*(15-5) + 100*(3-5) = 1800 300 300 300*(15-5) = 3000

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