Question

The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows: ALTERNATIVE PRECIPITATION LOW NORMAL HIGH Do Nothing (100 ) 100 300 Expand 350 500 200 Build New 750 300 0 If he feels the chances of low, normal, and high precipitation are 30 percent, 20 percent, and 50 percent respectively, what are expected long-run profits for the alternative he will select?

Answer 1

In case of doing nothing, the long run profits will be $70,000 with low precipitation, $80,000 with normal precipitation and $150,000 with high precipitation; in case of expanding the long run profits they will be $140,000 with low precipitation, $280,000 with normal precipitation and $250,000 with high precipitation; and in case of building a new one, the long run profits will be $525,000 with low precipitation, $250,000 with normal precipitation and $0 with high precipitation.

Calculus

Given that the operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing, and he estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows:

ALTERNATIVE PRECIPITATION

• LOW --- Do Nothing = 100 --- Expand = 200 --- Build New = 750
• NORMAL --- Do Nothing = 100 ---Expand = 350 --- Build New = 300
• HIGH --- Do Nothing = 300 --- Expand = 500 --- Build New = 0

If he feels the chances of low, normal, and high precipitation are 30 percent, 20 percent, and 50 percent respectively, to determine what are expected long-run profits for the alternative he will select, the following calculation must be performed:

Low =

• Do nothing = 100 - 100 x 0.3 = 100 - 30 = 70
• Expand = 200 - 200 x 0.3 = 200 - 60 = 140
• Build new = 750 - 750 x 0.3 = 750 - 225 = 525

Normal =

• Do nothing = 100 - 100 x 0.2 = 100 - 20 = 80
• Expand = 350 - 350 x 0.2 = 350 - 70 = 280
• Build new = 300 - 300 x 0.2 = 300 - 60 = 240

High =

• Do nothing = 300 - 300 x 0.5 = 300 - 150 = 150
• Expand = 500 - 500 x 0.5 = 500 - 250 = 250
• Build new = 0

Therefore, in case of doing nothing, the long run profits will be $70,000 with low precipitation, $80,000 with normal precipitation and $150,000 with high precipitation; in case of expanding the long run profits they will be $140,000 with low precipitation, $280,000 with normal precipitation and $250,000 with high precipitation; and in case of building a new one, the long run profits will be $525,000 with low precipitation, $250,000 with normal precipitation and $0 with high precipitation.

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