Acompany that manufactures racing boats estimates that the profit for selling its brand is given by the following equation. p(b) = -25b3 + 750b2 + 2,500b what is the least number of racing boats, b, that must be manufactured to make a profit of $75,000?

Step-by-step explanation:

This equation shows the income obtained based on the number of boats sold. We want to know the minimum number of boats that must be sold to obtain $ 75 000.

Then we must equalize the equation to 75 000 and clear b.

3 solutions will be obtained (because it is a polynomial of degree 3), and the lowest value will be taken.

Now we need to solve the equation, for that we seek to factor the polynomial

we divide the equation by -25

We take common factor b

We take out common factor (b-30)

Finally the solutions are:

b = 10 and b = -10

We take the least positive solution (because you can not produce -10 boats)

Finally b = 10

The smallest number of boats that must be produced to make a profit of $ 75,000 is 10 boats.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

4x and 6y

im not sure though