P(x) = R(x) - C(x)
= .4x^2 - 29x + 44 +.6x^2 - 19x
= x^2 - 48x + 44
this parabola cuts the x-axis at
x = 47.065 and a negative
Since x represents pencils, x>0
So this parabola will be above the x-axis for x>47
x of vertex is -b/(2a)
= 48/2 = 24
P(24) = -532
the vertex is (24,-532)
they will not make any profit until x > 47
The Yellow Pencil Company sells the best pencils ever made. If the cost of producing
x hundred pencils is given by C(x)=0.4x^2-29x+44 and if the revenue generated from the sale of x hundred pencils is R(x)=-0.6x^2+19x. Money is in thousands of dollars.
(a) Show all work to find the profit function, P(x)
(b) Show all work (use the formula) to find the vertex of the profit function and
interpret its meaning in the context of this problem.
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