Calculating Profit Relationship in Lamp Production

A company manufactures two types of lamps: Desk and Floor lamps. The production cost for each type of lamp is as follows:

• Desk lamps cost $15 each to produce.
• Floor lamps cost $25 each to produce.

These lamps are sold for $30 each. The company aims to cover its fixed costs of $1,200 monthly with its sales revenue from both types of lamps.

If the company produces $x$ Desk lamps and $y$ Floor lamps, the revenue generated from these lamps can be expressed as:

$$ R = 30(x + y) $$

The profit, which is the revenue minus the production costs, can be expressed as:

$$ P = R - C $$

where the costs can be expressed as:

$$ C = 15x + 25y + 1200 $$

To achieve a monthly profit of at least $600, set up an inequality that defines the relationship between $x$ and $y$. What is the value of $y$ when $x$ is 40?