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

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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

naivlingr 2021-05-09 Answered

The annual profit for a company that manufactures cell phine accessories can be modeled by the function

P (x) = - 0.0001 x^{2} + 70 x + 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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irwchh

Answered 2021-05-10 Author has 102 answers

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:
$x = - (\frac{70}{2 (- 0.0001)}) = 350000$
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:
$P (350000) = - 0.0001 {(350000)}^{2} + 70 (350000) + 125000$
$P (350000) = 12262500$
So, the maximum profit is $12,262,500.

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