Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A certain company's main source of income is selling cloth bracelets. The company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by: P(x)=-2x^(2)+16 x-24 What is the maximum profit that the company can earn? thousand dollars

A certain company's main source of income is selling cloth bracelets.\newlineThe company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by:\newlineP(x)=−2x2+16x−24P(x)=-2x^{2}+16x-24\newlineWhat is the maximum profit that the company can earn?\newlinethousand dollars

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Solve quadratic equations: word problemsright chevron icon

Full solution

Q. A certain company's main source of income is selling cloth bracelets.\newlineThe company's annual profit (in thousands of dollars) as a function of the price of a bracelet (in dollars) is modeled by:\newlineP(x)=−2x2+16x−24P(x)=-2x^{2}+16x-24\newlineWhat is the maximum profit that the company can earn?\newlinethousand dollars
  1. Identify profit function: Identify the profit function.\newlineThe profit function is given by P(x)=−2x2+16x−24P(x) = -2x^2 + 16x - 24, where P(x)P(x) is the profit in thousands of dollars and xx is the price of a bracelet in dollars.
  2. Recognize quadratic equation form: Recognize that the profit function is a quadratic equation in the form of P(x)=ax2+bx+cP(x) = ax^2 + bx + c, where a=−2a = -2, b=16b = 16, and c=−24c = -24.\newlineSince the coefficient of x2x^2 is negative (a=−2a = -2), the parabola opens downward, which means the vertex of the parabola will give the maximum profit.
  3. Calculate vertex x-coordinate: Calculate the x-coordinate of the vertex using the formula x=−b2ax = -\frac{b}{2a}.\newlineFor the given function, a=−2a = -2 and b=16b = 16, so x=−162⋅−2=−16−4=4x = -\frac{16}{2 \cdot -2} = -\frac{16}{-4} = 4.
  4. Substitute x-coordinate into profit function: Substitute the x-coordinate back into the profit function to find the maximum profit.\newlineP(4)=−2(4)2+16(4)−24=−2(16)+64−24=−32+64−24=32−24=8P(4) = -2(4)^2 + 16(4) - 24 = -2(16) + 64 - 24 = -32 + 64 - 24 = 32 - 24 = 8.
  5. Interpret the result: Interpret the result.\newlineThe maximum profit that the company can earn is $\(8\) \text{ thousand dollars}.

More problems from Solve quadratic equations: word problems

Question
Solve for v v .\newlinev2+8v+12=0 v^2+8v+12=0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinev= v=_____
Get tutor helpright-arrow

Posted 3 months ago

Question
Solve for u u .\newlineu2=9 u^2 = 9 \newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlineu= u = _____ or u= u = _____
Get tutor helpright-arrow

Posted 9 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinek2−20k+_____k^2 - 20k + \_\_\_\_\_
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve by completing the square.\newlineu2−24u−23=0u^2 - 24u - 23 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`u` = ________ or `u` =______
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the discriminant. \newline2q2−9q+8=02q^2 - 9q + 8 = 0\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve the system of equations.\newliney=22x−38 y = 22x - 38 \newliney=x2+11x−14 y = x^2 + 11x - 14 \newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) \newline(_,_) (\_,\_)
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for aa.\newline(a+5)(a+1)=0(a + 5)(a + 1) = 0\newlineWrite your answers as integers or as proper or improper fractions in simplest form.\newlinea=a = _____ or a=a = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Let p=x2−7 p=x^{2}-7 . Which equation is equivalent to (x2−7)2−4x2+28=5 (x^{2}-7)^{2}-4x^{2}+28=5 in terms of p p ? Choose 11 answer: \newline(A) p2−4p+23=0 p^{2}-4p+23=0 \newline(B) p2+4p−5=0 p^{2}+4p-5=0 \newline(C) p2−4p−5=0 p^{2}-4p-5=0 \newline(D) p2+4p+23=0 p^{2}+4p+23=0
Get tutor helpright-arrow

Posted 8 months ago

Question
Let m=2x+3m=2x+3. Which equation is equivalent to (2x+3)2−14x−21=−6(2x+3)^{2}-14x-21=-6 in terms of mm? Choose 11 answer: \newline(A) m2+7m+6=0m^{2}+7m+6=0 \newline(B) m2−7m−15=0m^{2}-7m-15=0 \newline(C) m2−7m+6=0m^{2}-7m+6=0 \newline(D) m2+7m−15=0m^{2}+7m-15=0
Get tutor helpright-arrow

Posted 8 months ago

Question
Let m=x2+3m=x^{2}+3. Which equation is equivalent to (x2+3)2+7x2+21=−10(x^{2}+3)^{2}+7x^{2}+21=-10 in terms of mm? Choose 11 answer:\newline(A) m2−7m+31=0m^{2}-7m+31=0\newline(B) m2+7m+31=0m^{2}+7m+31=0\newline(C) m2−7m+10=0m^{2}-7m+10=0\newline(D) m2+7m+10=0m^{2}+7m+10=0
Get tutor helpright-arrow

Posted 9 months ago

View all (43)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant