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A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per day, and p is price. The total cost function of the company is given by c = (30+5x) 2 where x is previously defined, and c is total cost.

Find the revenue and marginal revenue functions [Hint: revenue is price multiplied by quantity i.e. revenue = price × quantity]

Respuesta :

Answer:

The revenue function is

[tex]580x-10x^{2}[/tex]

The marginal revenue function is

[tex]580-20x[/tex]

Step-by-step explanation:

We have [tex]p=580-10x[/tex] where [tex]x[/tex] is the number of cakes sold per day and [tex]p[/tex] is the price.

Also, we have [tex]c=(30+5x)2[/tex] where [tex]x[/tex] is also the number of cakes and [tex]c[/tex] is the total cost.

The revenue would be

[tex](580-10x)x=580x-10x^{2}[/tex]

The marginal revenue would be the derivative of the revenue function

[tex]\frac{d}{dx}[580x-10x^{2} ] =580-20x[/tex]

Therefore, the answers are [tex]580x-10x^{2}[/tex] and [tex]580-20x[/tex], respectively.

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