Linear-Quadratic Systems — Quiz Answers

How many units need to be sold to maximize the company's revenue?

Which graph represents the system of equations? y=x^2−2⁢x+1 y=x+5

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+15⁢x−28 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=4⁢x How many units must the company sell to break even?

Jamar owns a clothing store. His fixed costs are $⁢800 per month, and it costs $⁢10 to produce each item. Your revenue is $⁢0 when 0 items are sold and $⁢0 when 150 items are sold due to market saturation. The maximum revenue occurs when 75 items are sold. Write a system of equations for the linear cost function, C⁡(x) , and a quadratic revenue function, R⁡(x) , where x represents the number of items sold.

What are the break-even points?

Part of the system of equations has been graphed. Graph the linear equation. y=x^2+2⁢x−3 y=−x−3

A software company has fixed monthly expenses of $⁢10,000 and a variable cost of $⁢100 per software license sold. Due to market capacity, revenue is $⁢0 when 0 licenses are sold and $⁢0 when 200 licenses are sold. The maximum revenue occurs when 100 licenses are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the number of software licenses sold?

What are the break-even points?

How many units need to be sold to maximize the store's revenue?

When does the maximum revenue occur?

A farmer sells organic apples at a local market. The fixed costs are $⁢800 per season, and the variable cost is $⁢1 per kilogram of apples sold. The revenue is $⁢0 when 0 kg or 160 kg of apples are sold due to market limitations. The maximum revenue occurs when 80 kg of apples are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the kilograms of apples sold?

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+12⁢x−18 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=3⁢x How many units must the company sell to break even?

Part of the system of equations has been graphed. Graph the linear equation. y=x^2−4 y=x−2

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+9⁢x−10 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=2⁢x How many units must the company sell to break even?

When does the maximum revenue occur?

A farmer sells organic apples at a local market. The fixed costs are $⁢800 per season, and the variable cost is $⁢1 per kilogram of apples sold. The revenue is $⁢0 when 0 kg or 160 kg of apples are sold due to market limitations. The maximum revenue occurs when 80 kg of apples are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the kilograms of apples sold?

How many units must the restaurant sell to break even?

When does the maximum revenue occur?

How many units must the restaurant sell to break even?

Part of the system of equations has been graphed. Graph the linear equation. y=x^2−2⁢x y=−x+6