Question

Consider the following set of constraints: -2X ≤ -176; -12Y ≤ -1056; 0.5 X + 12Y ≥1056, and 2X + 2Y ≤ 176. Pick a right statement for this problem:

a. Feasible region does not exist.

b. Feasible region is defined by a single point.

c. Feasible solution space is represented by a line, and multiple feasible solutions are available.

d. Solution to this problem cannot be found without the objective function.

e. All of the answers are incorrect.

Answer 1

The feasible region for the provided set of constraints -2X ≤ -176; -12Y ≤ -1056; 0.5 X + 12Y ≥ 1056, and 2X + 2Y ≤ 176 is defined by the single point where X and Y both equal 88.

Step-by-step explanation:

When considering the following set of constraints: -2X ≤ -176; -12Y ≤ -1056; 0.5 X + 12Y ≥ 1056, and 2X + 2Y ≤ 176, it's clear that these inequalities describe a system of linear inequalities and represent certain regions on a graph. After simplifying, we get X ≥ 88, Y ≥ 88, 0.5X + 12Y ≥ 1056, and X + Y ≤ 88. By graphing these inequalities, we can identify the feasible region where all these inequalities overlap. If such a region exists, it could be a point, a line, or a polygon area.

Looking at the inequalities, -2X ≤ -176 and -12Y ≤ -1056 imply that X and Y must be equal or greater than 88. However, 2X + 2Y ≤ 176 implies that X and Y, when added together, cannot exceed 88. This means X and Y must both be exactly 88 to satisfy all equations. Thus, the feasible region is defined by a single point where X and Y both are equal to 88.