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Suppose a manufacturing plant is considering three options for expansion. The first one is to expand into a new plant (large), the second to add on third-shift to the daily schedule (medium) and the third to do nothing (small). There are three possibilities for demand. These are high, medium, and low with the probability of .5 (H), .25 (M), .25 (L) of occurring. Suppose that the profits for the expansion plans are as follows (respective to high, medium, low demand). The large expansion profits are $100000, $10000,-$10000, the medium expansion choice $40000, $40000, $5000 and the small expansion choice $15000, $15000, $15000. a. What is the highest EMV? b. What is EVwPI?c. What is the organization willing to pay for perfect information?d. Which of the expansion plans should the manager choose?

Respuesta :

Answer:

a. $50,000

b. $77,500

c. $27,500

d. Large expansion or plant

Explanation:

a. What is the highest Expected Monetary Value (EMV)?

1. EMV of Large expansion = ($100000×0.50) + ($10000×0.25) + (-$10000×0.25)

EMV of Large expansion =

2. EMV of Medium expansion = ($40000×0.50) + ($40000×0.25) + ($5000×0.25)

EMV of Medium expansion = $31,250

3. EMV of Small expansion = ($15000×0.50) + ($15000×0.25) + ($15000×0.25)

EMV of Small expansion = $15,000

The highest EMV is $50,000 which is the EMV of Large expansion.

b. What is Expected Value with Perfect Information (EVwPI)?

EVwPI is obtained by adding together the expected value of the highest profit from each of the expansions as follows:

EVwPI = ($100000×0.50) + ($40000×0.50) + ($15000×0.50)

EVwPI = $77,500

c. What is the organization willing to pay for perfect information?

This requires the calculation of Expected Value of Perfect Information (EVPI). This can be obtained as follows:

EVPI = EVwPI - EVwoPI

Where EVwoPI denotes Expected Value without Perfect Information and it is is the highest EMV of $50,000 which is the EMV of Large expansion obtained in a above.

Substituting the figures, we have:

EVPI = $77,500 - $50,000 = $27,500

d. Which of the expansion plans should the manager choose?

The manager should choose the large expansion because it has the highest or maximum EMV of $50,000.

Answer:

1a $50000

1b is the price that an individual is willing to pay to get perfect information

1c $35125

1d Choose large expansion

Explanation:

Large expansion

(0.5×100000)+(0.25×100000)+(0.25×-100000)

=$50000

Medium expansion

(0.5×40000)+(0.25×40000)+(0.25×5000)

=$31250

Small Expansion

(0.5×15)+(0.25×15000)+(0.25×15000)

=$15000

EMV= $500000

       

1b EPwPI is the price that a and individula is willing to pay to get perfect information

1c

Large expansion

(0.5×10000)+(0.25×40000)+(0.25×15000)

=$18750

Medium expansion

(0.5×10000)+(0.25×40000)+(0.25×15000)

=$18750

Small Expansion

(0.5×-10000)+(0.25×5000)+(0.25×15000)

=$-1125

EV= $18750+$18750-1125

        =$36375

EPwPI = 50000- 36375

            =$35125

1d They should choose large expansion as it has the highest expected return.

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