Problema Solution
Macro Manufacturing estimates that its profit P in hundreds of dollars is P= - 3x^2+30x-2
where x is the number of units produced in thousands. How many units must be produced to obtain the maximum profit?
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Answer provided by our tutors
we must find the maximum of the parabolic function:
P= - 3x^2+30x-2
since the quotient in front of x^2 is -3<0 the function has maximum in the vertex:
x max = - b/2a, where a = -3, b = 30
x max = -30/(2(-3))
x max = 5
5 units must be produced to obtain maximum profit
You can also see the solution by drawing the graph of the function: y = - 3x^2+30x-2
click here to see the graph of the function y = - 3x^2+30x-2