Applied Mathematics

Linear Programming

Medium

The feasible reason for the constraints $x \geq 0$ , $x + y \leq 1$ and $x - y \leq 1$ , is situated in :

(A) I and II quadrant only

(B) I Quadrant

(C) II and IV Quadrant

(D) IV Quadrant

(E) I , II , III and IV Quadrant

Choose the correct answer from the option given below :

A , D only

B , D only

B , c only

A , C only

✅ Correct Option: 2

$x \geq 0$ restricts to the right half plane (Quadrants I and IV).

Testing (0.3, 0.3) in Q-I: all three constraints satisfied.

Testing (0.3, -0.3) in Q-IV: $x+y = 0 \leq 1$ and $x-y = 0.6 \leq 1$ , all satisfied.

Thus the feasible region lies in Quadrants I and IV, matching statements B and D.

Note: The original key marks (3) which has a lowercase typo 'c'; mathematically B and D are the correct pair, so we select option (2).

2023: 11 Aug Shift 1

Objective function $Z = 200x + 500y$ , subject to constraint, $x + 2y \geq 10, 3x + 4y \leq 24$ , $x \geq 0, y \geq 0$ - (iii), the minimum value of Z is :

2026: 14 May Shift 2

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	In a L.P.P the objective function is always	I.	Finite
B.	Feasible region for an L.P.P is always a	II.	Convex set
C.	In an L.P.P having bounded feasible region, the maximum value of the objective function $z = ax + by$ is always	III.	Linear
D.	Feasible region is the set of points which satisfy	IV.	All the given constraints

Choose the correct answer from the options given below:

2023: 11 Aug Shift 1

The corner points of feasible region determined by the following system of linear inequalities $2x + y \leq 10, x + 3y \leq 15, x \geq 0, y \geq 0$ are $(0,0), (5,0), (3,4)$ and $(0,5)$ , then the relation between p and Q so that minimum of Z occurs both points $(3,4)$ and $(0,5)$ is :

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. A solution that does not satisfy all the constraints is called	I. Linear
B. The objective function in an LPP is	II. Convex polygon
C. Linear inequalities or equations on the variables of LPP are called	III. Infeasible solution
D. The feasible region in an LPP, formed by the convex combinations of the corner points, is called	IV. Constraints

Choose the correct answer from the options given below:

2023: 15 June Shift 2

The minimum value of $z = 3x + 6y$ subject to the constraints $2x + 3y \leq 180$ , $x + y \geq 60$ , $x \geq 3y$ , $x \geq 0$ , $y \geq 0$ is :

2023: 15 June Shift 2

A carpenter earns a profit of ₹ 50 and ₹ 80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as :

Required	Chair	Table	Available quantity
Wood	3	5	150
Labour	1	2	56

The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively :

Solution

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