a certain companys main source of income is selling cloth bracelets. the companys annual profit (in…
a certain companys main source of income is selling cloth bracelets. the companys annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by: $p(x)=-2x^{2}+16x - 24$. what is the maximum profit that the company can earn? \n\nblank thousand dollars\n\nshow calculator
Answer
Explanation:
Step1: Identify the function type
The profit function $P(x)=-2x^{2}+16x - 24$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-2$, $b = 16$, $c=-24$.
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 $a=-2$ and $b = 16$ into the formula, we have $x=-\frac{16}{2\times(-2)}=\frac{-16}{-4}=4$.
Step3: Find the maximum profit
Substitute $x = 4$ into the profit function $P(x)$. So $P(4)=-2\times(4)^{2}+16\times4-24=-2\times16 + 64-24=-32+64 - 24=8$.
Answer:
8