Your Company Manufactures Two Models of Stereo Speakers, the Ultra $q _ { 1 } \left( p _ { 1 } , p _ { 2 } \right) = 50,000 - 100 p _ { 1 } + 10 p _ { 2 }$

Your company manufactures two models of stereo speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive then more people will buy the other. If p₁ is the price per pair of the Ultra Mini and p₂ is the price of the Big Stack, demand for the Ultra Mini is given by $q _ { 1 } \left( p _ { 1 } , p _ { 2 } \right) = 50,000 - 100 p _ { 1 } + 10 p _ { 2 }$
Where q₁ represents the number of pairs of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by
$q _ { 2 } \left( p _ { 1 } , p _ { 2 } \right) = 150,000 + 10 p _ { 1 } - 100 p _ { 2 }$
Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue.

Round your answer to the nearest dollar.

A) $798 for Ultra Mini and $275 for Big Stack
B) $428 for Ultra Mini and $783 for Big Stack
C) $275 for Ultra Mini and $798 for Big Stack
D) $328 for Ultra Mini and $783 for Big Stack
E) $783 for Ultra Mini and $328 for Big Stack