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Sagot :
Answer:
Explanation:
To solve this problem, we'll construct a decision tree to visualize the different options and their associated payoffs based on the probabilities of demand being low, average, or high.
Let's denote the options as follows:
- S: Small facility
- M: Medium facility
- L: Large facility
Here's the decision tree:
```
/ Low (0.25)
/
S ----<---- Average (0.40)
/ \ \
/ \ \
Low / \ Average \ High
/ \ \
/ \ \
$18,000 $75,000 $75,000
(S) (S) / \
/ \
$60,000 (M) $125,000 (L)
(M) (L)
/ Low (0.25)
/
M ----<---- Average (0.40)
/ \ \
/ \ \
Low / \ Average \ High
/ \ \
/ \ \
-$25,000 $140,000 $150,000
(M) (M) / \
/ \
$145,000 (L) $220,000 (L)
(L) (L)
/ Low (0.25)
/
L ----<---- Average (0.40)
/ \ \
/ \ \
Low / \ Average \ High
/ \ \
/ \ \
-$60,000 $125,000 $220,000
(L) (L) (L)
```
To achieve the highest expected payoff, management should choose the option with the highest expected value.
Based on the decision tree and the probabilities given:
- Expected payoff for a Small facility: \( 0.25 \times 18000 + 0.40 \times 75000 + 0.35 \times 75000 = 62250 \)
- Expected payoff for a Medium facility: \( 0.25 \times (-25000) + 0.40 \times 140000 + 0.35 \times 150000 = 111750 \)
- Expected payoff for a Large facility: \( 0.25 \times (-60000) + 0.40 \times 125000 + 0.35 \times 220000 = 101500 \)
Thus, management should choose to build a Large facility to achieve the highest expected payoff.
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