A car dealership estimates that the total weekly sales of its most popular model is a function of the car’s list price, p, and the interest rate in percent, i, offered by the manufacturer. The approximate weekly sales are given by f(p, i) = 99p – 0.5pi – 0.0025p²

a. Find the weekly sales if the average list price is $19,400 and the manufacturer is offering an 8% interest rate.

b. Find and interpret f_p(p, i) and f_i(p, i)

c. What would be the effect on weekly sales if the price is $19,400 and interest rates rise from 8% to 9%?