Question

A gas station sells 1400 gallons of gasoline per hour if it charges $ 2.40 per gallon but only 1200 gallons per hour if it charges $ 2.95 pergallon. Assuming a linear model(a) How many gallons would be sold per hour of the price is $ 2.55 per gallon?Answer:(b) What must the gasoline price be in order to sell 1100 gallons per hour?Answer: $(c) Compute the revenue taken at the four prices mentioned in this problem -- 2.40, 2.55,2.95andyouranswertopart(b). Whichpricegivesthemostrevenue? Answer:

Answer 1

Let y represent the number of gallons sold per hour

Let x represent the cost per gallon

From the information given in the question,

`\begin{gathered} y_1=1400,x_1=2.4 \\ y_2=1200,x_2=2.95 \end{gathered}`

Since the model is assumed to be a linear model, we can use the equation of a straight line to calculate the model

`\begin{gathered} (y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1) \\ (1200-1400)/(2.95-2.4)=(y-1400)/(x-2.4) \end{gathered}`
`\begin{gathered} (-200)/(0.55)=(y-1400)/(x-2.4) \\ 0.55y-770=-200x+480 \\ 0.55y=-200x+480+770 \\ 0.55y=-200x+1250 \end{gathered}`

(a) How many gallons would be sold per hour of the price is $ 2.55 per gallon?

Put x = 2.55 into the equation above

0.55y = -200x + 1250

0.55y = -200(2.55) + 1250

0.55y = -510 + 1250

0.55y = 740

y= 740/0.55

y= 1345.45

1345.45 gallons would be sold per hour if the price is $ 2.55 per gallon

(b) What must the gasoline price be in order to sell 1100 gallons per hour?

Put y = 1100 into the equation

0.55y = -200x + 1250

0.55(1100) = -200x + 1250

605 = -200x + 1250

200x = 1250- 605

200x = 645

x = 645/200

x=3.225

In order to sell 1100 gallons per hour, the price of the gasoline must be $3.225

(C)Compute the revenue taken at the four prices mentioned in this problem -- 2.40, 2.55,

2.95andyouranswertopart(b).