A gas station sells 1600 gallons of gasoline per hour if it charges $ 2.70 per gallon but only 900 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 $ 2.90 per gallon?
Answer:
(b) What must the gasoline price be in order to sell 1300 gallons per hour?
Answer:

Let +g+ = gallons of gas sold per hour
Let +p+ = price per gallon in dollars
Plot +g+ on the vertical axis
Plot +p+ on the horizontal
use the point slope formula
+%28+g+-+800+%29+%2F+%28+p+-+2.4+%29+=+%28+900+-+800+%29+%2F+%28+2.15+-+2.4+%29+
+%28+g+-+800+%29+%2F+%28+p+-+2.4+%29+=+100+%2F+%28-.25%29+
+%28+g+-+800+%29+%2F+%28+p+-+2.4+%29+=+-400+
+g+-+800+=+-400%2A%28+p+-+2.4+%29+
+g+-+800+=+-400p+%2B+960+
+g+=+-400p+%2B+1760+
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(a)
+g+=+-400%2A2.35+%2B+1760+
+g+=+-940+%2B+1760+
+g+=+820+
820 gallons/hr would be sold
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(b)
+g+=+-400p+%2B+1760+
+1600+=+-400p+%2B+1760+
+400p+=+1760+-+1600+
+400p+=+160+
+p+=+.4+
The price must be $ .40 / gallon to sell 1600 gallons/hr
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(c)
(1) +2.15%2A900+=+1935+
Revenue = $ 1,935
(2) +2.4%2A800+=+1920+
Revenue = $ 1,920
(3) +2.35%2A820+=+1927+
Revenue = $ 1,927
+.4%2A1600+=+640+
Revenue = $640
$2.15 / gallon gives the most revenue