Question to test your Graphing Systems of Inequalities knowledge

Question

Graph the following system of inequalities, and evaluate the objective function at each corner of the graphed region. Then, identify the values of x and y for which the maximum value is found.

Inequality system: z = x + 8y with constraints for x and y.

Accepted Answer

z(0, 6) = 48; z(0, 8) = 64; z(10, 0) = 10; z(5, 0) = 5; maximum value: 64 at x = 0 and y = 8

Graph of a system of inequalities showing feasible region with vertices at (0,6), (0,8), (5,0), (10,0).

Answer

z(0, 6) = 20; z(0, 8) = 45; z(10, 0) = 15; z(5, 0) = 32; maximum value: 45 at x = 0 and y = 8

Graph of a system of inequalities showing feasible region with vertices at (0,6), (0,8), (5,0), (10,0).

Answer

z(0, 6) = 48; z(0, 10) = 80; z(9, 0) = 9; z(7, 0) = 7; maximum value: 80 at x = 0 and y = 10

Graph of a system of inequalities showing feasible region with vertices at (0,10), (0,6), (7,0), (9,0).

Answer

z(0, 6) = 36; z(0, 10) = 92; z(9, 0) = 15; z(7, 0) = 12; maximum value: 92 at x = 0 and y = 10

Graph of a system of inequalities showing feasible region with vertices at (0,10), (0,6), (7,0), (9,0).

Graphing Systems of Inequalities: Study with Video Lessons, Practice Problems & Examples

Graph the following system of inequalities, and evaluate the objective function at each corner of the graphed region. Then, identify the values of x and y for which the maximum value is found.