Answer! an independent home builder’s annual profit, in thousands of dollars, can be modeled by the function p left parenthesis x right parenthesis equals 5.152 x cubed minus 143 x squared plus 1102 x minus 1673, where x is the number of houses built in a year. his company can build at most 13 houses in a year. find the y-intercept and explain what it means in this context. find the x-intercept(s) for the profit equation given in number 1 and explain what they mean in this context.

Solution-

The profit function given in the question,

Where,

x = the number of houses built in a year

We can calculate y-intercept by putting x=0, so

y-intercept is -1673, i.e when x=0 or the number of houses built is 0, their profit is -1673. Actually it is not the profit, but loss. So if they don't build any house, they will lose $1673

We can calculate x-intercept or zeros by putting y=0, so

Calculating the zeros by graphing calculator, they are as follows,

x-intercept shows that they need to built at least 15 (as number house can not be fraction) houses, in order to start profiting. Even though they start profiting after building 2 houses, but then the profit starts decreasing and reaches 0 again and so does happen after building 11th house. (It might happen due to the other costs and investments used for building the houses ). But after finally building 15th house they start profiting.

choice b is correct

step-by-step explanation:

we have been given the following system of linear inequalities;

we are required to graphically determine the solution to these system of inequalities. using a graphing tool, the solution is as shown in the attachment below;