# The annual profit for a company that manufactures cell phine accessories can be modeled by the function P(x)=-0.0001x^2+70x+12500 where x is the numbe

The annual profit for a company that manufactures cell phine accessories can be modeled by the function
$P\left(x\right)=-0.0001{x}^{2}+70x+12500$ where x is the number of units sold and P is the total profit in dollars.
a. What sales level maximizes the companys
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a.The sales level needed to maximize the annual profit is the x-value of the vertex of the quadratic function. The highest point is the vertex of the parabola represented by the equation in the form y=ax2+bx+c with a<0 where the x-coordinate is given by x=−b2a.
Substitute a=−0.0001 and b=70:
$x=-\left(\frac{70}{2\left(-0.0001\right)}\right)=350000$
So, 350,000 units will maximize the profit.
b.Using the x-value from part (a) and the profit function, the maximum annual profit is:
$P\left(350000\right)=-0.0001{\left(350000\right)}^{2}+70\left(350000\right)+125000$
$P\left(350000\right)=12262500$
So, the maximum profit is \$12,262,500.