Your Company Manufactures Two Models of Stereo Speakers, the Ultra $q _ { 1 } \left( p _ { 1 } , p _ { 2 } \right) = 200,000 - 100 p _ { 1 } + 10 p _ { 2 }$

Multiple Choice

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 $q _ { 1 } \left( p _ { 1 } , p _ { 2 } \right) = 200,000 - 100 p _ { 1 } + 10 p _ { 2 }$
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) $874 for Ultra Mini and $1,033 for Big Stack
B) $1,033 for Ultra Mini and $874 for Big Stack
C) $1,186 for Ultra Mini and $859 for Big Stack
D) $1,086 for Ultra Mini and $859 for Big Stack
E) $859 for Ultra Mini and $1,086 for Big Stack