Question

New York is getting ready for a busy tourist season. They want to increase production or at least produce the same amount as last year, depending on the demand level for the coming season. NY estimates the probabilities for high, medium and low demands to be 0.5, 0.3, 0.2 respectively. These estimates are based on forcasts provided by the local tourist bureau. If they increase production, the profits corresponding to high, medium and low demands will be $800000, $400000 and $200000 respectively. If they do not increase production, the profits corresponding to the demands levels are 600000, 300000 and 200000 respectively/ Should NY increase production or maintain there existing levels?

Answer 1

To answer this question , it is important to find the expected value of the profits:

Scenario - A :

Probability (high demand) = 0.5

Probability (medium demand) = 0.3

Probability (low demand) = 0.2

Profits (high demand) = $800000

Profits (medium demand) = $400000

Profits (low demand) = $200000

Expected Profit:

[Probability(high demand) × Profit(high demand) + Probability(medium demand) × Profit(medium demand) + Probability(low demand) × Profit(low demand)]

=> 800000(0.5) + 400000(0.3) + 200000(0.2)

=> 400000 + 120000 + 40000

=> $560000

Scenario - B:

Profits (high demand) = $600000

Profits (medium demand) = $300000

Profits (low demand) = $200000

Expected Profit (Scenario- B):

=> 600000(0.5) + 300000(0.3) + 200000(0.2)

=> 300000 + 90000 + 40000

=> $430000

As expected Profit is higher in Scenario-A , (increasing production),so, New York must increase the production.