To determine the feasible region's corner points, we need to solve the system of inequalities:

$10x + 16y \geq 6000$ $10x + 8y \leq 3600$ $x, y \geq 0$

Step 1: Find the x- and y- intercepts for each constraint

First constraint: $10x + 16y = 6000$

• x-intercept: Set $y = 0$ $10x = 6000 \Rightarrow x = 600$ Point: $(600, 0)$

• y-intercept: Set $x = 0$ $16y = 6000 \Rightarrow y = 375$ Point: $(0, 375)$

Second constraint: $10x + 8y = 3600$

• x-intercept: Set $y = 0$ $10x = 3600 \Rightarrow x = 360$ Point: $(360, 0)$

• y-intercept: Set $x = 0$ $8y = 3600 \Rightarrow y = 450$ Point: $(0, 450)$

Step 2: Solve for the Intersection of the Two Lines

Solve the system: $10x + 16y = 6000$ $10x + 8y = 3600$

Subtract the second equation from the first: $(10x + 16y) - (10x + 8y) = 6000 - 3600$

$8y = 2400$

$y = 300$

Substituting $y = 300$ into $10x + 8(300) = 3600$:

$10x + 2400 = 3600$

$10x = 1200 \Rightarrow x = 120$

Point: $(120, 300)$

Step 3: Identify Feasible Region and Corner Points

The feasible region is bounded by:

• $(0, 450)$
• $(0, 375)$
• $(120, 300)$

Thus, the correct answer is:

(c) $(0, 450), (0, 375), (120, 300)$

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Related Questions:

1. How do you graph the feasible region for a linear programming problem?
2. How do you find the optimal solution for the objective function $40x + 30y$?
3. What method can be used to solve a system of two linear equations graphically?
4. How does the feasible region change if an additional constraint is added?
5. How do you determine if a given point is in the feasible region?

Tip:

When solving linear programming problems, always check if the feasible region is bounded or unbounded, as this affects whether an optimal solution exists!