Question

Identify the feasible region for the following set of

constraints:
1 .3x-2y >(or)= 0
2 .2x-y <(or)= 200
3 .x<(or)= 150
4 .x,y >(or)= 0

Answer 1

The feasible region is the intersection of the areas satisfying each of the inequalities, located in the first quadrant of the coordinate system, forming a polygon or irregular shape.

Step-by-step explanation:

To identify the feasible region for the given set of constraints, we need to graph each inequality and find the intersection of these areas.

1. For the inequality 3x - 2y ≥ 0, we can sketch the line 3x - 2y = 0. This line represents all points where 3x = 2y, or y = 1.5x. The feasible area would be above this line since we want y to be less than or equal to 1.5x.
2. For 2x - y ≤ 200, we draw the line 2x - y = 200 and shade the area below it since we want y to be greater than or equal to 2x - 200.
3. The inequality x ≤ 150 is a vertical line at x = 150, with the feasible region to its left.
4. The constraints x, y ≥ 0 define the first quadrant of the coordinate system, where both x and y are non-negative.

The feasible region is the common area that satisfies all four constraints and is typically a polygon or irregular shape located in the first quadrant, bounded by the lines and axes drawn.

Answer 2

The feasible region is the area where all the shaded regions overlap. It's the region that satisfies all the given constraints simultaneously: it includes the area below the line y = 0.15 y=0.15x, above the line y = 2x − 200 y=2x−200, to the left of x=150, and within the first quadrant.