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The daily quantity demanded of unleaded gasoline in a regional market can be represented as Q = 100 - l Op + E, where p E [O, 8], and E is a random variable having a probability density given by f( e) = .025/1-20,201 (e) Quantity demanded, Q, is measured in thousands of gal­ lons, and price, p, is measured in dollars.

a. What is the probability of the quantity demanded being greater than 70,000 gallons if price is equal to $4? if price is equal to $3?

b. If the average variable cost of supplying Q amount of unleaded gasoline is given by C( Q) = Q-5/2, de· fine a random variable that can be used to represent the daily profit above variable cost from the sale of unleaded gasoline.

c. Ifprice is set equal to $4, what is the probability that there will be a positive profit above variable cost on a given day? What if price is set to $3? to $5?

d. If price is set to $6, what is the probability that quantity demanded will equal 40,000 gallons?

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  • Category:- Statistics and Probability
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