-save AssorinertProgress Eracice Another Versi 41 points SitzPreCak MyAo The ori

Question

-save AssorinertProgress Eracice Another Versi 41 points SitzPreCak MyAo The original function used to model the cost of producing x PortaBoys Game Systems was Cx)-80x 150. While developing their newest game, Sasquatch Atackl, the makers of the PortaBoy revised ax) = .03x3-4.5x2 + 226x + 250, Market research indicates that the demand function p(x)--15x their cost function using a cubic polynomial. The new cost of producing x PortaBoys is given by indicates that the demand function p(x) 15x250 remains unchanged. F ind the x that maximizes the profit made by producing and selling x PortaBoys. (Round your answer to the nearest whole number.) production level x that maximizes the profit made by producing and selling x Port PortaBoys Additional Materials DReading Im Cortana. Ask me 8 0 2

Explanation / Answer

C(x) = 0.3x^3-4.5x^2+226x+250

p(x) = -1.5x+250

Revenue = p(x)*x =-1.5x^2+250x

Profit = z(x) = -0.3x^3+3x^2+24x-250

z'(x) = -0.9x^2+6x+24

z"(x) = -0.18x+6

Max at x = 6/0.9(2) = 3 1/3

as units cannot be in fractin round off to 3 or 4.

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Degree =4

Leading term = x^4

Leading coeff =1

Constant term = 12

End behaviouir is f(x) tends to infinity as x tends to -infinity(since x is of even degree leading term)

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