Question

A bicycle company produces y bikes at a cost represented by the polynomial y^2 + 10y + 100,000. The revenue for y bicycles is represented by 2y^2 + 10y + 500. Show your work!

Answer 1

To find the equilibrium level of output for the bicycle company, we set the cost equal to the revenue and solve for y. However, the quadratic equation does not have real solutions, indicating that there is no equilibrium level of output.

Step-by-step explanation:

The cost of producing y bikes is represented by the polynomial y^2 + 10y + 100,000. The revenue for y bicycles is represented by the polynomial 2y^2 + 10y + 500. To find the equilibrium level of output, we set the cost equal to the revenue and solve for y.

y^2 + 10y + 100,000 = 2y^2 + 10y + 500

Combining like terms and simplifying, we get:

y^2 - 2y^2 + 10y - 10y + 100,000 - 500 = 0

-y^2 + 99,500 = 0

Since the degree of the quadratic equation is negative, it does not have real solutions. Therefore, there is no equilibrium level of output for this bicycle company.