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

of the three mortgage options that demarco and tanya have to choose from, the balloon payment mortgage would be their best option, over adjustable payment and fixed payment plans.ultimately, the balloon payment plan would save demarco and tanya overall, in interest, would cost less monthly, and they would only have to make these payments for 8 years, opposing to 30 years for adjustable or fixed payment plans. 

overall, demarco and tanya would save $80,811 if they chose balloon payments over fixed payments, and would save $116,711 if they choose balloon payments over adjustable payments. benefits with choosing fixed payments over adjustable payments is that, in the end, the payments will still be $836.30 a month, while with adjustable payments, the initial monthly payments will be $763.38 to $1082.70 a month, ultimately leading to a more costly purchase. benefits with choosing fixed payments over balloon payments are not present. benefits in choosing adjustable payments over is that it has a lower interest rate, and starts with lower monthly payments initially. benefits in choosing adjustable payments over balloon payments include a lower interest rate, and lower initial monthly payments. benefits in choosing balloon payments over fixed payments include lower interest rates, lower overall price, lower monthly payments, takes less time to pay off, and does not require a downpayment. benefits in choosing balloon payments over adjustable payments include, lower monthly payments (when averaged), takes less time to pay off, and lower overall price.

hence, option c, balloon payments, is the best option for demarco and tanya to make this purchase, for it will save them a minimum of $80811, and a maximum of $116,711.