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 socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: P(x)=-3(x-5)^(2)+12 What is the maximum profit that the company can earn? million dollars

A certain company's main source of income is selling socks.\newlineThe company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by:\newlineP(x)=−3(x−5)2+12P(x)=-3(x-5)^{2}+12\newlineWhat is the maximum profit that the company can earn?\newlinemillion 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 socks.\newlineThe company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by:\newlineP(x)=−3(x−5)2+12P(x)=-3(x-5)^{2}+12\newlineWhat is the maximum profit that the company can earn?\newlinemillion dollars
  1. Identify profit function: Identify the profit function and the form it is in.\newlineThe profit function is given by P(x)=−3(x−5)2+12P(x) = -3(x - 5)^2 + 12. This is a quadratic function in the form of P(x)=a(x−h)2+kP(x) = a(x - h)^2 + k, where (h,k)(h, k) is the vertex of the parabola.
  2. Determine vertex of parabola: Determine the vertex of the parabola.\newlineSince the coefficient of the squared term is negative (−3-3), the parabola opens downwards, which means the vertex represents the maximum point on the graph. The vertex (h,k)(h, k) can be read directly from the equation as (5,12)(5, 12).
  3. Interpret vertex in context: Interpret the vertex in the context of the problem.\newlineThe vertex (5,12) (5, 12) tells us that the maximum profit, which is k k in the vertex form, is $12 \$12 million, and it occurs when the price of a pair of socks is $5 \$5 .
  4. State maximum profit: State the maximum profit the company can earn.\newlineThe maximum profit the company can earn is $12 million\$12\,\text{million}.

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 1 month 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 2 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 2 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 2 months ago

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

Posted 2 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 1 month 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 2 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 2 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 2 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 2 months ago

View all (42)