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Mathematics

1 answer:

sveta [45]4 years ago

6 0

Where the points intersect should be the solution to systems of equations.

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A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

jonny [76]

Answer:

x = $36 , y = $ 838

Step-by-step explanation:

Solution:-

The company makes a profit of $y by selling widgets at a price of $x. The profit model is represented by a parabola ( quadratic ) equation as follows:

$y = -x^2 + 72x -458$

We are to determine the profit maximizing selling price ( x ) and the corresponding maximum profit ( y ).

From the properties of a parabola equation of the form:

$y = ax^2 + bx + c$

The vertex ( turning point ) or maximum/minimum point is given as:

$x = -\frac{b}{2a} \\\\x = -\frac{72}{-2} = 36$

The profit maximizing selling price of widgets would be x = $36. To determine the corresponding profit ( y ) we will plug in x = 36 in the given quadratic model as follows:

$y ( 36 ) = - ( 36 )^2 + 72 ( 36 ) - 458\\\\y ( 36 ) = -1296 + 2592 - 458\\\\y ( 36 ) = 838$