The course is Quantitive Research Methods and the book is Quantitive Analysis fo

Question

The course is Quantitive Research Methods and the book is Quantitive Analysis for Management (12 ed.) (Render, Stair, Jr., Hanna, & Hale, 2015). Boston, MA: Pearson.

Problem 3-27. 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 daily 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 that the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case.

a) Draw a decision table for this problem.

b) What do you recommend?

Explanation / Answer

A.

Step 1 of the decision table is as follows:

Step 2 of the decision table is as follows:

B.

Expected profit when 100 case ordered = .3*1000 + .4*(-600) + .3*(-2200) = -$600

Expected profit when 200 case ordered = .3*800 + .4*2000 + .3*400 = $1160

Expected profit when 300 case ordered = .3*600 + .4*1800 + .3*3000 = $1800

Since, the highest expected payoff is $1800 that takes place when 300 case is ordered, so recommendation will be to 300 case to be ordered.

Alternative Demand of 100 case Demand of 200 case Demand of300 case 100 case ordered (15-5)*100 (15-5)*100 - 16*100 (15-5)*100 - 16*200 200 case ordered (15-5)*100 + (3-5)*100 (15-5)*200 (15-5)*200 - 16*100 300 case ordered (15-5)*100 + (3-5)*200 (15-5)*200 + (3-5)*100 (15-5)*300 Probability 0.3 0.4 0.3

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