Gadget Production Profit and Constraints

A company produces two types of gadgets: Type A and Type B. The profits from selling these gadgets can be modeled by the equation:

$$ P = 50x + 30y $$

where:

• $$ P $$ is the total profit in dollars,
• $$ x $$ is the number of Type A gadgets sold,
• $$ y $$ is the number of Type B gadgets sold.

The company has a goal of achieving a profit of at least $3000. Additionally, the constraints on production are:

• $$ x + 2y ext{ ≤ } 100 $$ (maximum production capacity),
• $$ x ext{ ≥ } 0 $$ and $$ y ext{ ≥ } 0 $$ (non-negativity constraints).

Which of the following pairs of $(x, y)$ satisfies both the profit requirement and the production constraints?