An independent home builder’s annual profit, in thousands of dollars, can be modeled by the function p(x)=5.152x^3 -143x^2+1102x-1673, where x is the number of houses built in a year. his company can build at most 13 houses in a years.
A.) How many should the builder construct in order to have a profit of at least $400,000?
B.) How many houses should the builder construct in order to maximize profit?