Question

A market analyst has projected that the cost of producing d dog leashes will be given by the polynomial 9000 + 3.2d. The revenue generated from the sale of d dog leashes will be given by the polynomial d(15 - 0.00005d). Which polynomial expression represents the profit earned from producing, and selling d dog leashes?

A. - 0.0016d³ + 47.55d² + 135,000d
B. 0.00005d² - 18.2d - 9000
C. - 0.00005d² + 11.8d - 9000
D. - 0.00005d² - 11.8d + 9000

Answer 1

C.
`-0.00005d^2+11.8d-9000`

Explanation:

Given:

Cost Price for producing 'd' dog lashes =
`9000+3.2d`

Revenue Generated from selling 'd' dog lashes =
`d(15-0.00005d)`

We need to find the profit earned from producing and selling 'd' dog lashes.

Solution:

Now we know that;

profit earned from producing and selling 'd' dog lashes can be calculated by Subtracting Cost Price for producing 'd' dog lashes from Revenue Generated from selling 'd' dog lashes.

framing in equation form we get;

Profit earned =
`d(15-0.00005d)-(9000+3.2d)`

Now Applying Distributive property we get;

Profit earned =
`15d-0.00005d^2-9000-3.2d`

Now Combining like terms we get;

Profit earned =
`-0.00005d^2+15d-3.2d-9000`

Profit earned =
`-0.00005d^2+11.8d-9000`

Hence Profit earned from producing and selling 'd' dog lashes is
`-0.00005d^2+11.8d-9000`.