Question

For the following shaded region, the linear constraints are:

• A. \( 5x + 9y \leq 90, \quad x + y \geq 4, \quad y \geq 8, \quad x, y \geq 0 \)
• B. \( 5x + 9y \geq 90, \quad x + y \leq 4, \quad y \leq 8, \quad x, y \geq 0 \)
• C. \( 5x + 9y \geq 90, \quad x + y \geq 4, \quad y \geq 8, \quad x, y \geq 0 \)
• D. \( 5x + 9y \leq 90, \quad x + y \geq 4, \quad y \leq 8, \quad x, y \geq 0 \)

Hint:

When determining linear constraints for a shaded region, carefully observe the lines and boundary conditions for the region's limits.

Answer 1

The Correct Option is D

Step 1: Analyze the constraints.
From the image of the shaded region, we can deduce the constraints based on the lines and regions formed by the given conditions. These include the boundaries of the axes, the line equations, and the limits on \( x \) and \( y \).
Step 2: Conclusion.
Thus, the linear constraints are \( 5x + 9y \leq 90, \quad x + y \geq 4, \quad y \leq 8, \quad x, y \geq 0 \), corresponding to option (D).