<h3>Answer: Revenue decreases by 23.2%</h3>
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Work Shown:
x = demand
p = price
Solve for the demand x when the price is p = 4.50 dollars.
x+500p = 3500
x+500(4.50) = 3500
x+2250 = 3500
x = 3500-2250
x = 1250
If the price is $4.50, then the demand is 1250 (ie 1250 people will want a hamburger)
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Compute the revenue
Revenue = (price per item)*(number of items sold)
Revenue = p*x
Revenue = (4.50)*(1250)
Revenue = 5625
If the price per burger is $4.50, then the revenue is $5,625.
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Let's increase the price by 20%. To do this, multiply by 1.20
1.20*4.50 = 5.40
The price of the burger is now $5.40
Let's see what x will become after we plug in p = 5.40
x+500p = 3500
x+500(5.40) = 3500
x+2700 = 3500
x = 3500-2700
x = 800
The demand has dropped to 800
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Next compute the new revenue
Revenue = (price per item)*(number of items sold)
Revenue = p*x
Revenue = (5.40)*(800)
Revenue = 4320
The revenue is now $4,320
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Lastly, find the percent change from the old revenue ($5,625) to the new revenue ($4,320)
A = old value = 5625
B = new value = 4320
C = percent change from A to B
C = 100*(B-A)/A
C = 100*(4320-5625)/5625
C = 100*(-1305/5625)
C = 100*(-0.232)
C = -23.2%
The negative C value indicates a percent decrease.
<h3>Revenue has decreased by 23.2%</h3>
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