the function $f(x)=-(x - 20)(x - 100)$ represents a companys monthly profit as a function of $x$, the number…

the function $f(x)=-(x - 20)(x - 100)$ represents a companys monthly profit as a function of $x$, the number of purchase orders received. which number of purchase orders will generate the greatest profit?\n20\n60\n80\n100

the function $f(x)=-(x - 20)(x - 100)$ represents a companys monthly profit as a function of $x$, the number of purchase orders received. which number of purchase orders will generate the greatest profit?\n20\n60\n80\n100

Answer

Answer:

B. 60

Explanation:

Step1: Expand the function

$f(x)=-(x - 20)(x - 100)=-(x^{2}-100x - 20x+2000)=-x^{2}+120x - 2000$

Step2: Identify the formula for vertex of parabola

For a quadratic function $y = ax^{2}+bx + c$, the x - coordinate of the vertex is $x=-\frac{b}{2a}$. Here $a=-1$ and $b = 120$.

Step3: Calculate the x - coordinate of the vertex

$x=-\frac{120}{2\times(-1)}=\frac{-120}{-2}=60$ The number of purchase orders $x = 60$ will generate the greatest profit.