Question

Given below is the price-demand equation for the production of tennis shoes where x is the number of pairs of tennis shoes that can be sold at a price of $p dollars. p = 35 − x (a) Determine the revenue function and the marginal revenue function.

Answer 1

R(x) = 35x - x^{2}

MR(x) = 35 - 2x

Step-by-step explanation:

Given that,

price-demand equation: p = 35 − x

x is the number of pairs of tennis shoes

Selling price of a pair of shoes = $p

Revenue is calculated by multiplying selling price with the number of units sold.

Revenue function: R(x) = Selling price × Number of units sold

= px

= (35 - x) x

=
`35x-x^(2)`

Marginal revenue function is calculated by differentiating the revenue function.

Now, differentiating R(x) with respect to x,

Marginal revenue function: MR(x) = 35 - 2x