A gas station sells 1500 gallons of gasoline per hour if it

A gas station sells 1500 gallons of gasoline per hour if it charges $2.70 per gallon but only 800 gallons per hour if it charges $2.80 per gallon. Assuming a linear model (a) How many gallons would be sold per hour of the price is $2.75 per gallon? (b) What must the gasoline price be in order to sell 1500 gallons per hour? Round to the nearest cent. (c) You can find revenue by multiplying the price by the number of gallons sold. Compute the revenue taken at the four prices mentioned in this problem --$ 2.70, $ 2.75, $ 2.80 and your answer to part (b). Which price gives the most revenue? Round to the nearest cent.

Solution

from the statement we have 2 points

(2.70, 1500 ) and ( 2.80 , 800 )

finding equaton from the 2 points

slope = -7000

therefore , equation is

y = -7000x + 20400

where, y is the amount of galons sold and x is the price per gallon

so, if price if $ 2.75 , amount of galons sold is

y = -7000(2.75) + 20400

y = 1150 gallons

b) 1500 = -7000x + 20400

solving for x

x = 2.7

therefore, 1500 gallons must be sold for $ 2.7

c) revenue for $ 2.70 = 2.70*1500 = $ 4050

revenue for $ 2.75 = 2.75*1150 = $3162.5

revenue for $ 2.80 = 2.80* 800 = $ 2240

so maximum revenue comes from $ 2.70