Question

The profit P (in thousands of dollars) for an educational publisher can be modeled by P 52b31 5b21b where b is the number of workbooks printed (in thousands). Currently, the publisher prints 5000 workbooks and makes a profit of $5000. What lesser number of workbooks could the publisher print and still yield the same profit?

Answer 1

The lesser number of workbooks are 1,000

Explanation:

The correct question is

The profit P (in thousands of dollars) for an educational publisher can be modeled by P=-b³+5b²+b where b is the number of workbooks printed (in thousands). Currently, the publisher prints 5000 workbooks and makes a profit of $5000. What lesser number of workbooks could the publisher print and still yield the same profit?

we have

`P=-b^3+5b^2+b`

For
`P=\$5,000`

substitute in the equation and solve for b

Remember that the profit and the number of workbooks is in thousands

so

P=5

`5=-b^3+5b^2+b`

Using a graphing tool

Solve the cubic function

The solutions are

x=-1

x=1

x=5

therefore

The lesser number of workbooks are 1,000

Verify

For b=1

`P=-(1)^3+5(1)^2+1`

`P=5` -----> is in thousands

so

`P=\$5,000` ----> is ok