SOLUTION: Help is urgently needed.
The profit P(in millions of pesos) for a manufacturer of tablets can be modeled by {{{ P=-4x^3+12x^2+16x }}} where x is the number of tablets produced (
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Question 995708: Help is urgently needed.
The profit P(in millions of pesos) for a manufacturer of tablets can be modeled by where x is the number of tablets produced (in millions). Currently, the company produces 3 million tablets and makes a profit of 48,000,000 pesos. What lesser number of tablets could the company produce and still make the same profit?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
to find out the point where profit is equal to 0, just set the equation equal to 0 and solve.
you get:
-4x^3 + 12x^2 + 16x = 0
factor out the gcf to get:
(-4x) * (x^2 - 3x - 4) = 0
factor x^2 - 3x - 4 to get:
(-4x) * (x-4) * (x+1) = 0
set each of these factors equal to 0 and solve for x to get:
x = 0, x = 4, x = -1.
x represents number of tablets.
x = 0 leads to a profit of 0 but that's trivial.
x = -1 is invalid because number of tablets can't be negative.
only valid answer is that profit is 0 when x = 4.
you have 3 zero crossing points and you want to see whether profit is positive or negative between them.
the only intervals that are valid are the intervals between x = 0 and x = 4, and the interval where x is greater than 4.
it turns out that x is positive in the interval between x = 0 and x = 4 only.
it is negative otherwise.
if you look at the graph, you will see that the same profit is made when x = 2 and when x = 3.
that can be seen by drawing a horizontal line at y = 48 and the intersection will be at x = 2 and x = 3.
the grpah of your equation is shown below along with the line of y = 48.
results on the graph are in millions.
when x = 2 million, you make a 48 million profit.
when x = 3 million, you make a 48 million profit.
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