# Mr. Ripoff's gas station can sell 355 gallons of gas per day at \$4.00 per gallon and 164 gallons at \$5.00 per gallon. Mr. Ripoff pays \$1.20 pergallon for the gas and has daily fixed costs of \$500.Find the unit price p that will maximize revenue:Find the unit price p that will maximize profit:What is the maximum possible daily profit?dollars per gallon.dollarsdollars.

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Step 1

Let q be the gallons of gas sold per day.

Daily cost incurred C(q)=1.20q + 500.

Next we find the relationship between price at which gas is sold(p) and the quantity sold daily(q).

The relationship is linear and we are provided two points on the graph , namely, (355,4) and (164,5).

From this , the relation is determined as 191p+q=1119.

=>q=1119-191p

Revenue(R)=q*p=1119p-191p^2

Revenue will be maximun when dR/dp=0

Step 2

Calculating dR/dp:

Step 3

i) For maximum Revenue, pric...

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