Question

A gas station sells 1500 gallons of gasoline per hour if it charges $ 2.20 per gallon but only 1300 gallons per hour if it charges $ 2.95 per gallon. Assuming a linear model

(a) How many gallons would be sold per hour of the price is $ 2.25 per gallon?
Answer:

(b) What must the gasoline price be in order to sell 800 gallons per hour?
Answer: $

(c) Compute the revenue taken at the four prices mentioned in this problem -- $ 2.20, $ 2.25, $ 2.95 and your answer to part (b). Which price gives the most revenue?
Answer: $

Answer 1

SOLUTION:

From given data,

A gas station sells 1500 gallons of gasoline per hour if it charges $ 2.20 per gallon but only 1300 gallons per hour if it charges $ 2.95 per gallon. Assuming a linear model

given that,

charges $ 2.20 per gallo

gas station sells 1500 gallons

charges $ 2.95 per gallon

(a) How many gallons would be sold per hour of the price is $ 2.25 per gallon

We need to set this up as a linear equation. First we need to find the slope of the line by taking the two points (2.20, 1500) and (2.95,1300) and solving

m = (1300-1500)/ (2.95-2.20)

= -200/0.75

= -267

Now using the point slope formula y-y₁= m(x-x₁) we get

y-1500= -267(x -2.20)

y= -267 x + 2087.4

So now if you substitute 2.25 for x you get

y= -267 (2.25) + 2087.4

= 1486.65 gallons sold per hour

(b) What must the gasoline price be in order to sell 800 gallons per hour?

To find the price you take the linear equation and solve for x

800= -267 x + 2087.4

(800-2087.4)/(-267) = x

x = 4.82

$4.82 is the price that gasoline has to have to only sell 800 gallons per hour.

(c) Compute the revenue taken at the four prices mentioned in this problem . $ 2.20, $ 2.25, $ 2.95 and your answer to part (b). Which price gives the most revenue?

The revenues can be calculated by taking gallons sold times the price

2.20*1500 =3300

2.25*1486.65 =3344.9625

2.95*1300=3835

4.82*800=3856

The highest price of $4.82 gives the highest revenue.