A manufacturer of dishware is considering modernizing its current manufacturing facility which makes the most popular line of dishware. The modernization of the facility will dramatically decrease the manufacturing cost for large production volumes.

The annual demand for this line of dishware along with its probability distribution is given in Table 1 (column 1 and 2 respectively). The current variable manufacturing cost per each unit produced varies according to the demand volume (as given in column 3 of Table 1). Each unit is sold for $35 per unit. The existing facility has annual fixed operating cost of $200,000.

After modernization, the manufacturing facility will require higher annual fixed operating cost of $240,000. Variable manufacturing cost per units will change according to the last column in Table 1 (notice that it is considerably lower for the higher demand volumes).

Demand
(units per year)

Probability

Current variable cost ($
per unit)

New Variable cost ($ per
unit)

8,000

0.5

7.75

9.40

10,000

0.2

5.00

5.20

15,000

0.2

5.40

3.80

20,000

0.1

7.50

4.90

Table
1.

Should the company modernize its current facility based on the annual net expected profits?

3. DECISION ANALYSIS.

A company is deciding whether or not to go ahead with a project. If the project is successful, the company will make $500,000 profit. If the project fails, the company’s net loss will be $250,000. The probability of the project’s success is 0.5.

a) If perfect information about the success or failure of this project was available, how much would this information be worth?

The company occasionally hires consultant to update their estimates of success/failure. Consultant predicts either success or failure for the project; in either case the company must decide whether or not to go ahead with the project. The company is considering hiring Harry who charges $10,000 for his services.

The probability of Harry predicting success is 0.5. The following probabilities were determined based on Harry’s previous predictions:

P(project succeeds when Harry predicts success) = 0.8
P(project fails when Harry predicts failure) = 0.8

b) Should Harry be hired? If yes, what is the value of his prediction to the company?