Problema Solution
John owns a hot dog stand. He has found that his profit is represented by the equation P(x)=-x^2+50x+67, with P being profit and x the number of hot dogs. How many hot dogs must he sell to earn the most profit?
Answer provided by our tutors
we must find the maximum of the parabolic function:
P(x)=-x^2+50x+67
since the quotient in front of x^2 is -1<0 the function has maximum in the vertex:
x max = - b/2a, where a = -1, b = 50
x max = -50/(2(-1))
x max = 25
John must sell 25 hotdogs to earn most profit.
You can also see the solution by drawing the graph of the function: y = -x^2+50x+67
click here to see the graph of the function y = -x^2+50x+67