Find the Maximum/Minimum Value R(p)=-2.5p^2+700p

$R (p) = - 2.5 p^{2} + 700 p$

Step 1

The maximum of a quadratic function occurs at $x = - \frac{b}{2 a}$ . If $a$ is negative, the maximum value of the function is $f (- \frac{b}{2 a})$ .

$f_{max}$ $p = a p^{2} + b p + c$ occurs at $p = - \frac{b}{2 a}$

Step 2

Find the value of $p = - \frac{b}{2 a}$ .

Substitute in the values of $a$ and $b$ .

$p = - \frac{700}{2 (- 2.5)}$

Remove parentheses.

$p = - \frac{700}{2 (- 2.5)}$

Simplify $- \frac{700}{2 (- 2.5)}$ .

Cancel the common factor of $700$ and $2$ .

Factor $2$ out of $700$ .

$p = - \frac{2 \cdot 350}{2 \cdot - 2.5}$

Cancel the common factors.

Factor $2$ out of $2 \cdot - 2.5$ .

$p = - \frac{2 \cdot 350}{2 (- 2.5)}$

Cancel the common factor.

$p = - \frac{2 \cdot 350}{2 \cdot - 2.5}$

Rewrite the expression.

$p = - \frac{350}{- 2.5}$

Simplify the expression.

Divide $350$ by $- 2.5$ .

$p = - - 140$

Multiply $- 1$ by $- 140$ .

$p = 140$

Step 3

Evaluate $f (140)$ .

Replace the variable $p$ with $140$ in the expression.

$R (140) = - 2.5 {(140)}^{2} + 700 (140)$

Simplify the result.

Simplify each term.

Raise $140$ to the power of $2$ .

$R (140) = - 2.5 \cdot 19600 + 700 (140)$

Multiply $- 2.5$ by $19600$ .

$R (140) = - 49000 + 700 (140)$

Multiply $700$ by $140$ .

$R (140) = - 49000 + 98000$

Add $- 49000$ and $98000$ .

$R (140) = 49000$

The final answer is $49000$ .

$49000$

Step 4

Use the $x$ and $y$ values to find where the maximum occurs.

$(140, 49000)$

Step 5

Find the Maximum/Minimum Value R(p)=-2.5p^2+700p

Related Questions

Support LCMGCF.com by disabling your adblocker.