1.) A gas station sells 1200 gallons of gasoline per hour if it charges $ 2.10 p

Question

1.) A gas station sells 1200 gallons of gasoline per hour if it charges $ 2.10 per gallon but only 1000 gallons per hour if it charges $ 2.90 per gallon. Assuming a linear model:

(a) How many gallons would be sold per hour if the price is $2.45 per gallon? Answer: _________

(b) What must the gasoline price be in order to sell 1300 gallons per hour? Answer: $ _________

(c) Compute the revenue taken at the four prices mentioned in this problem – $2.10, $2.45, $2.90 and your answer to part (b). $ __________

(d) Which price gives the most revenue? Answer: $ __________

Explanation / Answer

1200 Gallons sold when price is at $2.10

1000 Gallons sold when price is at $2.90

Calculate what is the change in gallones per change in cent

i.e., $1 increase in price, decreases gallons sold by (1200 - 1000) / ( 2.90 - 2.10) = 200 / 0.80 = 250

So 1 cent increase in price, decreases gallons sold by 250 / 100 = 2.5

a) Gallons sold at $2.45

2.45 is 35 cents more than 2.10, so gallons sold decreases by 2.5 * 35 = 87.5

So 1200 - 87.5 = 1112,5 gallons sold per hour

b) 1300 gallons will be sold when price is

1300 - 1200 = 100 gallons increase will occcer when 100 / 2.5 = 40 cents price is reduced

So 2.1 - 0.4 = $1.7

c) Revenue at price

2.10 => 2.1 * 1200 = 2520

2.90 => 2.9 * 1000 = 2900

2.45 => 2.45 * 1112.5 = 2725.6

d) Maximum revenue is generated at prices $3.44, $3.45, $3.46 when gallons sold per hour are 865, 862.5, 860 respectively. Revenue generated is 2975.6

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