The Top-Humid Company manufactures water containers for commercial humidifiers and vaporizers. The production processes for each product are similar but they require a different amount of time for blending and molding. For a vaporizer, it takes 12 hours of blending and 3 hours of molding. For a humidifier, it takes 5 hours of blending and 2.5 hours of molding.
There are up to 900 blending hours and 300 molding hours available for the coming production period. In particular, to ensure sufficient supplies, the company decides to manufacture at least 40 humidifiers and 20 vaporizer water containers. The company will earn a profit of $15 per humidifier and $23 per vaporizer.
Formulate a linear program model to maximize the profit during the next production period. (Define decision variables and write the objective function constraints.)