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.

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

MR(x) = 35 - 2x

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

                                      =

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

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