Question

If \( R_2 \) is the feasible region, then what are the other two non-trivial constraints?

Hint:

For alternative feasible regions, observe which inequalities reverse based on the region's boundaries and shading in the graph.

Answer 1

Region \( R_2 \) is defined by \( x + 2y \geq 100 \), \( x \geq 0 \), and \( y \geq 0 \), excluding the constraints of region \( R_1 \). The constraints, derived from the graph, are \( x + 2y \geq 100 \) and \( y - \frac{4}{3}x + \frac{80}{3} \leq 0 \).
Final Answer: The constraints for \( R_2 \) are: \[ x + 2y \geq 100 \quad {and} \quad y - \frac{4}{3}x + \frac{80}{3} \leq 0. \]