# Linear Programming

This is an MCQ-based quiz on Linear Programming.

This includes Covering problems, Minimum set cover, Minimum vertex cover, and Minimum edge cover.

Start Quiz

Feasible region in the set of points which satisfy

The objective functions Some the given constraints All of the given constraints None of these

A set of values of decision variables which satisfies the linear constraints and nn-negativity conditions of a L.P.P. is called its

Unbounded solution Optimum solution Feasible solution None of these

The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is

300 600 400 800

Objective function of a linear programming problem is

A constraint

Function to be obtimized

A relation between the variables

None of these

The corner points of the feasible region determined by the following system of linear inequalities: 2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = px + qy, where p, q > 0. Conditions on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is

p = 3q p = 2q p = q q = 3p.

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q> 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is Maximum of Z occurs at:

(5, 0) (6, 5) (6, 8) (4, 10).

The point which does not lie in the half-plane 2x+3y-12<0 is

(1,2)

(2,1)

(2,3)

(-3,2)

Maximize Z = 3x + 5y, subject to x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0

20 at (1, 0) 30 at (0, 6) 37 at (4, 5) 33 at (6, 3)

Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0

16 at (4, 0) 24 at (0, 4) 24 at (6, 0) 36 at (0, 6)

Maximize Z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0

59 at (9/2, 5/2) 42 at (6, 0) 49 at (7, 0) 57.2 at (0, 5.2)
Quiz/Test Summary
Title: Linear Programming
Questions: 10
Contributed by: 