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).
a. What is the expected average global price per pumpkin
b. how many pumpkins should the farmer harvest?
(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) Farmer formula for calculating quanttity is Q = 0.01P
Q = 0.01P
=> Put P = 7
=> Q = 0.01 (7)
=> Q = 0.07
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