Question

Consider the following linear program. Max 1A 2B - s.t. -4A + 3B ≤ 3 1A 1B ≤ 4 A, B ≥ 0 (a) Graph the feasible region for the problem. B B 15 15 10 10 / 5 face A 2 4 6 8 10 12 14 2 4 6 8 10 12 1

Answer 1

HereHere is the graph for the feasible region:Graph of feasible region for the given problem is shown below. It is formed by graphing the given two constraints.The first constraint is-4A + 3B ≤ 3Or, 4A - 3B ≥ -3We get the following graph by plotting the line 4A - 3B = -3 and then testing a point on the side of the line from which the origin (0,0) is visible. The half of the plane which satisfies this inequality is the feasible region.The second constraint is1A + 1B ≤ 4Or, A + B ≤ 4We get the following graph by plotting the line A + B = 4 and then testing a point on the side of the line from which the origin (0,0) is visible. The half of the plane which satisfies this inequality is the feasible region.The feasible region is shown below. The line 4A - 3B = -3 and A + B = 4 intersect at (3/5, 17/5).This point is obtained by solving the two equations simultaneously.