Answer to Question #81595 in Calculus for Cassandra

Question

The original function used to model the cost of producing x PortaBoys Game Systems was
C(x) = 80x + 150.
While developing their newest game, Sasquatch Attack!, the makers of the PortaBoy revised their cost function using a cubic polynomial. The new cost of producing x PortaBoys is given by
C(x) = .03x3 − 4.5x2 + 224x + 250.
Market research indicates that the demand function
p(x) = −1.5x + 250
remains unchanged. Find the production level x that maximizes the profit made by producing and selling x PortaBoys.