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Algebra
Pregunta

9. A board game company models the profit on its l...

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? 

Answer

(a)\(- 2x^{2} + 28x- 90= 0\)

(x-9)(x-5)=0

x1=9,x2=5

(b)The vertex coordinates of the parabola are\((- \frac{b}{2a},\frac{4ac- b^{2} }{4a}  )\)

\(- \frac{b}{2a} = 7\)

\(- 2\times 7^{2} + 28\times 7- 90= 8\)

max:8 millions of dollars

Solución
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