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

Answer:

The lesser number of workbooks are 1,000

Step-by-step 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