Step 1  :

Given that :

is the price in dollars.

is the quantity sold of a certain product .

The demand equation is .

Solve for .

.

Step 2  :

(a)

The revenue .

Substitute in .

Revenue .

Step 3  :

(b)

The quantity sold of a certain product .

Revenue .

The revenue if 15 units are sold is.

Step 4  :

(c)

The function is a quadratic function.

Compare the function with standard form of a quadratic function.

.

Since , the vertex is the highest point on the parabola.

The revenue is a maximum when the quantity sold of a certain product is .

Maximum revenue

Maximum revenue is

Step 5  :

(d)

The price .

Maximum revenue is at .

At , the company charge to maximum price.

The maximum price,

should the company charge to maximize the revenue.

Step 6 :

(e)

Graph and are on the same Cartesian plane.

Find where the graphs intersects.

The graph is shown below :

The graphs intersect at

From the graph the company should charge between to earn at least in revenue.