The price-demand equation for hamburgers at a fast food restaurant is given by the equation below. Currently the price of a hamburger is $4.50. If the price is
increased by 20% how will the revenue be affected?
x+500p = 3500
If the price is increased by 20%, the revenue will
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The given demand equation is a linear relationship through which it is possible to calculate the revenue

When the price is increased by 20%, the revenue decreases by 23.2%

Reason:

The given equation relating price and quantity is; x + 500·p = 3,500

The current price of a hamburger = $4.50

The effect on the revenue following a price increase of 20%

Solution;

Quantity, x = 3,500 - 500·p

Current quantity is therefore;

x = 3,500 - 500 × 4.5 = 1,250

Revenue = Price × Quantity demanded

The current revenue = $4.5 × 1,250 = $5,625

If the price increased 20%, we have;

New price = 1.2 × 4.5 = 5.4

The new increased price of the hamburger = $5.4

The new quantity demanded, x' = 3,500 - 500 × 5.4 = 800

The new revenue = $5.4 × 800 = $4,320

The change in revenue is therefore;

Therefore;

Therefore;

When the price is increased by 20%, the revenue decreases by 23.2%

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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.

50-38=12

step-by-step explanation: