Question

2. A pumpkin farmer has to decide how many pumpkins to harvest for the world market. There is a one-half probability that the average global price will be $ 4 per pumpkin, a one-quarter probability that it will be $ 8 and a one-quarter probability that it will be $12. His calculation formula is Q (quantity) = 0.01P (price).

What is a. the expected average global price per pumpkin and b. how many pumpkins should the farmer harvest?

Answer 1

(a) There is a one-half probability (i.e., 1/2)  that the average global price will be $ 4 per pumpkin, a one-quarter probability (i.e., 1/4)  that it will be $ 8 and a one-quarter probability (i.e., 1/4) that it will be $12.

=> Expected price = Σ(Price * Probability of price)

=> Expected price = ($4) * (1/2) + ($8) * (1/4) + ($12) * (1/4)

=>Expected price = $2 + $2 + $3

=> Expected price = $7

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(b) Q = 0.01P

=> Put P = 7

=> Q = 0.01 (7)

=> Q = 0.07