15. -/0.93 points details my notes sprecalc8 3.1.053. ask your teacher practice another a manufacturer finds…

15. -/0.93 points details my notes sprecalc8 3.1.053. ask your teacher practice another a manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function r(x)=100x - 0.2x², where the revenue r(x) is measured in dollars. what is the maximum revenue, and how many units should be manufactured to obtain this maximum? $ at units need help? read it watch it submit answer

15. -/0.93 points details my notes sprecalc8 3.1.053. ask your teacher practice another a manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function r(x)=100x - 0.2x², where the revenue r(x) is measured in dollars. what is the maximum revenue, and how many units should be manufactured to obtain this maximum? $ at units need help? read it watch it submit answer

Answer

Explanation:

Step1: Identify the function type

The revenue function $R(x)=100x - 0.2x^{2}$ is a quadratic - function in the form $y = ax^{2}+bx + c$, where $a=-0.2$, $b = 100$, and $c = 0$.

Step2: Find the x - value of the vertex

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is given by $x=-\frac{b}{2a}$. Substituting $a=-0.2$ and $b = 100$ into the formula, we have $x=-\frac{100}{2\times(-0.2)}=\frac{100}{0.4}=250$.

Step3: Find the maximum revenue

Substitute $x = 250$ into the revenue function $R(x)=100x-0.2x^{2}$. Then $R(250)=100\times250-0.2\times(250)^{2}=25000-0.2\times62500=25000 - 12500=12500$.

Answer:

$12500$, $250$