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

The revenue function is

`580x-10x^(2)`

The marginal revenue function is

`580-20x`

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

`(d)/(dx)[580x-10x^(2) ] =580-20x`

Therefore, the answers are
`580x-10x^(2)` and
`580-20x`, respectively.