What is the maximum possible profit?

Question:A company produces two types of products, A and B. Each product requires different amounts of raw material and labor. The company has a limited supply of 500 units of raw material and 600 hours of labor. The production of one unit of product A requires 2 units of raw material and 3 hours of labor, while the production of one unit of product B requires 4 units of raw material and 2 hours of labor. Each unit of product A generates a profit of $50, and each unit of product B generates a profit of $40.

Determine:

1. How many units of product A and product B should the company produce to maximize profit?
2. What is the maximum possible profit?

Constraints:

• Raw material constraint: $2x+4y500$
• Labor constraint: $3x+2y600$
• Non-negativity constraint: $x0,y0$

Where:

• $x$ is the number of units of product A produced.
• $y$ is the number of units of product B produced.

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