Question

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]

Answer 1

Answer:

The revenue function is

$580x-10x^{2}$

The marginal revenue function is

$580-20x$

Step-by-step explanation:

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

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

The revenue would be

$(580-10x)x=580x-10x^{2}$

The marginal revenue would be the derivative of the revenue function

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

Therefore, the answers are $580x-10x^{2}$ and $580-20x$, respectively.