Problema Solution
The profit P in millions of dollars for a tshirt manufacturer can be modeled by P=-x^3+4x^2+x where x is the number of tshirts produced in millions. currently, the company produces 4 million tshirts and makes a profit of $4,000,000. what lesser number of tshirts could the company produce and still make the same profit?
Answer provided by our tutors
will get the number by solving P=-x^3+4x^2+x for P = 4
-x^3+4x^2+x = 4
-x^3+4x^2+x - 4 = 0
and we know that one root of the cubic equation is x = 4
since -x^3+4x^2+x - 4 = -x^2(x - 4) + (x - 4) = (x - 4)(1 - x^2)
we need to find the positive roots of 1 - x^2 = 0
1 - x^2 = 0
x^2 = 1
x = 1
indeed for x = 1 we have for the profit P(1) = -1^2 + 4*1^2 + 1 = 4
the company will make a profit of $1,000,000 if it produces 1,000,000 t-shirts.