The function f(x) = -(x-20)(x - 100) represents a company's monthly profit as a function of x, the number of purchase
orders received. which number of purchase orders will generate the greatest profit?
20
60
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The number of purchase orders that will generate the greatest profit is 60 orders

Step-by-step explanation:

we have

This is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex represent the greatest profit

The x-coordinate of the vertex represent the number of purchase orders for the greatest profit

Convert the function in vertex form

Complete the square

Rewrite as perfect squares

The vertex is the the point (60,1,600)

therefore

The greatest profit is $1,600

The number of purchase orders that will generate the greatest profit is 60 orders