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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Asked Jan 20, 2019
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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 per
gallon 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.
dollars
dollars.
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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 per gallon 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. dollars dollars.

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Expert Answer

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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

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Step 2

Calculating dR/dp:

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Step 3

i) For maximum Revenue, pric...

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