Solve the Problem $\$ 2.50$ Each for Each 25 Cent Increase in the Price, the of Hot

Solve the problem.
-The stadium vending company finds that sales of hot dogs average 45,000 hot dogs per game when the hot dogs sell for $\$ 2.50$ each. For each 25 cent increase in the price, the sales per game drop by 2000 hot dogs. Determine a function $R ( x )$ that models the total revenue per game, where $x$ is the number of $\$ 0.25$ increases in the price of a hot dog.

A) $R ( x ) = - 500 x ^ { 2 } + 6250 x + 112,500$
B) $R ( x ) = 500 x ^ { 2 } + 6250 x - 112,500$
C) $R ( x ) = - 500 x ^ { 2 } + 14,250 x + 112,500$
D) $R ( x ) = - 500 x ^ { 2 } + 11,250 x + 112,500$