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

question 113

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 $q _ { 1 } \left( p _ { 1 } , p _ { 2 } \right) = 50,000 - 100 p _ { 1 } + 10 p _ { 2 }$
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

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Definitions:

Purchased

Acquired by paying money or its equivalent; involves obtaining ownership of a good or service in exchange for monetary value.

MAGI

MAGI stands for Modified Adjusted Gross Income, a measure used in the U.S. tax code to determine eligibility for certain tax benefits by modifying the adjusted gross income with specific additions or deductions.

Net Investment Income

The income received from investment assets (like stocks, bonds, mutual funds) after deducting related expenses.

Surtax

An additional tax levied on top of the base tax liability; often applied to income exceeding a certain threshold.