Mastering Linear Programming Concepts

Front

Formulate a linear programming problem for maximizing profit given the constraints: 2x + 3y ≤ 12, x ≥ 0, y ≥ 0.

Back

Maximize P = profit_A * x + profit_B * y subject to 2x + 3y ≤ 12, x ≥ 0, y ≥ 0.

Front

Graph the inequality 3x + 4y < 24 on a coordinate plane.

Back

Graph the dashed line through points (8, 0) and (0, 6) and shade below the line.

Front

Identify the feasible region for the constraints: x + y ≤ 10, x ≥ 0, y ≥ 0.

Back

The feasible region is the area in the first quadrant bounded by the axes and the line x + y = 10.

Front

Create a linear programming model for a factory producing two products with profit margins of $5 and $7, subject to resource constraints.

Back

Maximize Z = 5x + 7y, subject to 2x + 3y <= 100, x + 2y <= 80, x >= 0, y >= 0.

Front

Graph the inequality 2x - y ≥ 4 and shade the feasible region.

Back

Graph the line y = 2x - 4 with a solid line and shade the region below it.

Front

Determine the vertices of the feasible region defined by the inequalities: x + 2y ≤ 8, 3x + y ≤ 9, x ≥ 0, y ≥ 0.

Back

[(0, 0), (0, 4), (2, 3), (3, 0)]

Front

Formulate a linear programming problem to minimize costs given the constraints: 4x + 5y ≥ 20, x + 2y ≤ 10.

Back

Minimize C = cx + dy subject to 4x + 5y ≥ 20, x + 2y ≤ 10, x ≥ 0, y ≥ 0.

Front

Graph the system of inequalities: y ≤ 2x + 1, y ≥ -x + 3, and identify the feasible region.

Back

The feasible region is the area where the shaded regions of the two inequalities overlap.

Front

Maximize z = 3x + 2y subject to: x + y ≤ 5, x ≥ 0, y ≥ 0.

Back

(5, 0) with maximum z = 15

Front

How to determine if a point is in the feasible region defined by the inequalities: x + y ≤ 6, x - y ≥ 2, x ≥ 0, y ≥ 0?

Back

A point is in the feasible region if it satisfies all the inequalities.