Question

If \( R_1 \) is the feasible region, then what are the other two non-trivial constraints?

Hint:

To identify non-trivial constraints: 1. Observe the lines forming the boundary of the feasible region. 2. Derive the equations of these lines and check the direction of inequality from the graph.

Answer 1

Step 1: Given one non-trivial constraint is \( x + 2y \geq 100 \). From the graph: 
- The line passing through \( A(0, 50) \) and \( E(100, 0) \) corresponds to \( x + 2y = 100 \). 
- The line passing through \( B(20, 40) \) and \( C(50, 100) \) corresponds to \( y - \frac{4}{3}x + \frac{80}{3} \geq 0 \). 
- The line passing through \( C(50, 100) \) and \( D(0, 200) \) corresponds to \( y - 2x \leq 0 \). 
Final Answer: The other two non-trivial constraints are: \[ y - \frac{4}{3}x + \frac{80}{3} \geq 0 \quad {and} \quad y - 2x \leq 0. \]