A food manufacturer has to decide how many batches of a product to produce next week. If one batch is produced then a profit of $15,000 will be made. If two batches are produced then either a loss of $5,000 will be made if demand only equals one batch or a profit of $20,000 will be made if demand equals two batches. The manufacturer provisionally estimates the probabilities of these two outcomes to be 0.4 and 0.6 respectively. After making these estimates the manufacturer finds that a statistical demand forecasting method suggests that demand will equal two batches. In the past the method has correctly predicted demand in 60% of the weeks, irrespective of what the level of demand turned out to be. To maximize his expected profit, the manufacturer should:

Question

A food manufacturer has to decide how many batches of a product to produce next week.  If one batch is produced then a profit of $15,000 will be made.  If two batches are produced then either a loss of $5,000 will be made if demand only equals one batch or a profit of $20,000 will be made if demand equals two batches.  The manufacturer provisionally estimates the probabilities of these two outcomes to be 0.4 and 0.6 respectively.  After making these estimates the manufacturer finds that a statistical demand forecasting method suggests that demand will equal two batches.  In the past the method has correctly predicted demand in 60% of the weeks, irrespective of what the level of demand turned out to be.  To maximize his expected profit, the manufacturer should:
a)produce one batch
b)produce two batches
c) be indifferent between producing 1 or 2 bathces
d) seek further information as it is not possible to computer the expected profits from the information

Next, suppose that the manufacturer had to decide whether it was worth paying for the forecast of the statistical demand forecasting method before making his decision.  The expected value of imperfect information obtained from the method would have been:
a) 0
b) $2,700
c) $5,000
d) $7,800

Next, suppose that the statistical demand forecast always gave a correct indication.  The expected value of perfect information obtained from the method would have been:
a)0
b) $3,000
c) $6,000
d) $18,000

PsyDAG · Answer

We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.

Joy · Answer

The problem is I don't even know how to get started. My book is horrible at explaining the concept. My guess is 2 batches for the first question, but then I'm not sure how to figure out the next two.