The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=27(4)−x4, find the revenue if 12 units are sold. Round to two decimal places.

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Step-by-step explanation:

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The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=274−4x, find the revenue if 12 units are sold. Round to two decimal places.

Step one

given the following expression

Revenue

[tex]R(x)=xp(x)[/tex]

Unit price

[tex]p(x)=274-4x[/tex]

Required

the revenue when 12 units were sold

let us find the unit price for 12 units

[tex]p(x)=274-4x\\\\p(x)=274-4(12)\\\\p(x)=274-48\\\\p(x)=226[/tex]

Hence the unit price is$ 226

[tex]R(x)=xp(x)\\\\R(x)=12*226\\\\R(x)=2712[/tex]

Revenue is $2712

There is a revenue of $5.04 if 12 units are sold.

Revenue is the product of the number of units and the price per unit. It is given by:

Revenue = number of units * price per unit

Revenue = x * p(x)

Given that the price per unit is:

[tex]p(x)=27(4)^{-\frac{x}{4} }\\\\For\ x=12:\\\\\\p(12)=27(4)^{-\frac{12}{4} }=\$0.42[/tex]

Therefore the revenue is:

Revenue = x * p(x) = 12 * 0.42

Revenue = $5.04

Therefore there is a revenue of $5.04 if 12 units are sold.

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