Question

URGENT Q: A bicycle company produces y bicycles at a cost represented by the polynomial y² + 10y + 100,000. The revenue for y bicycles is represented by 2y^2 + 10y + 500. Find a polynomial that represents the company's profit. If the company only has enough materials to make 300 bicycles, should it make the bicycles?

Answer 1

The company should not make 300 bicycles.

Explanation:

Mathematically speaking, profit (
`P(y)`) equals the difference between revenue (
`R(y)`) and cost (
`C(y)`). That is:

`P(y) = R(y) - C(y)` (1)

If we know that
`R(y) = 2\cdot y^(2)+10\cdot y + 500` and
`C(y) = y^(2)+10\cdot y+100000`, then the profit function is:

`P(y) = 2\cdot y^(2)+10\cdot y +500 -y^(2)-10\cdot y -100000`

`P(y) = y^(2)-99500` (2)

The company can make the required amount of bicycles if and only if
`P(y) > 0`. If
`y = 300`, then the profit of company is:

`P(300) = 300^(2)-99500`

`P(300) = -9500`

The company should not make 300 bicycles.