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Answer :
Final answer:
To maximize profit, find the x-coordinate of the vertex of the quadratic function.
Explanation:
To maximize profit, we need to find the value of x that corresponds to the vertex of the quadratic function.
The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic function in the form of ax^2 + bx + c.
In this case, a = -10, b = 3500, and c = -66000.
Plugging in these values, we get
x = -3500 / (2*(-10))
= -3500 / (-20)
= 175.
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Answer: 175
Step-by-step explanation:
To find maximum, we need to find the vertex.
The x-value of the vertex is the number of automobiles that should be made and sold. The y-value is the maximum profit.
P(x) = -10x² + 3500x - 66,000
a=-10, b = 3500, c=-66,000
[tex]x=\dfrac{-b}{2a}[/tex]
[tex]x=\dfrac{-(3500)}{2(-10)}[/tex]
[tex]x = \dfrac{-3500}{-20}[/tex]
[tex]x = 175[/tex]
BONUS:
The maximum profit is: P(x) = -10(175)² + 3500(175) - 66,000
= -300,625 + 612,500 - 66,000
= 245,875
