The profit of a shoe company is modelled by the quadratic function \(P ( x ) = - 5 ( x - 4 ) ^ { 2 } + 45 ,\) where \(x\) is the number of pairs of shoes produced, in thousands, and \(P ( x )\) is the profit, in thousands of dollars. How many thousands of pairs of shoes will the company need to sell to earn a profit?
Pregunta
Answer
The company should sell greater than 1 thousand pairs of shoes to make a profit.
\(x> 1\)
Related Questions
Q:
9. A board game company models the profit on its latest board game using the quadratic relation
\( P = - 2 x ^ { 2 } + 28 x - 90 , \) where \( x \) is the number of games it produces in hundred thousands and \( P \) is the profit in millions of dollars.
a) What are the break-even points for the company?
b) What is the maximum profit that the company can earn?
Q:
The graph of \( y = f ( x ) \) is stretched horizontally by a factor of \( 5 \) , and reflected in the \( x \) -axis. What is the equation of the image graph in terms of \( f \) ?
A. \( y = - f ( 5 x ) \) C. \( y = - f ( \frac { 1 } { 5 } x ) \)
B. \( y = - \frac { 1 } { 5 } f ( x ) \) D. \( y = - 5 f ( x )\)