Final answer:
After graphing the inequalities 2x + 4y ≥ 100 and 1x + 8y ≤ 100 with nonnegativity constraints, the feasible region is determined to be unbounded as it extends infinitely in the first quadrant of the coordinate plane.
Step-by-step explanation:
To determine which statement about the feasible region of a linear programming problem is true, given the constraints 2x + 4y ≥ 100 and 1x + 8y ≤ 100, plus nonnegativity constraints on x and y, we must graph these inequalities on a coordinate plane.
The first inequality, 2x + 4y ≥ 100, is a half-plane above the line x + 2y = 50. The second inequality, 1x + 8y ≤ 100, creates another half-plane underneath the line x + 8y = 100. The nonnegativity constraints imply that x and y cannot be negative, confining the feasible region to the first quadrant of the coordinate plane.
By graphically representing these constraints, we find the feasible region to be the area that satisfies all constraints simultaneously. This region is not a single point or empty because there are multiple points that satisfy all conditions, nor is it bounded because as x tends towards infinity, y can still satisfy the inequality given the slope of the lines and the nonnegativity constraints. Therefore, the region continues indefinitely. Hence, the correct answer is The feasible region is an unbounded region.