Algebra

Linear Programming

Medium

core

A linear programming problem is as follows:

Minimize $z = 2x + 3y$

Subject to the constraints $x \ge 3, x \le 9, y \ge 0, x - y \ge 0, x + y \le 14$ . The feasible region has 5 corner points including

(0, 0) and (9, 5)

(14, 0) and (9, 0)

(7, 7) and (3, 3)

(3, 6) and (9, 5)

✅ Correct Option: 3

The constraints are:

$x \ge 3$ , $x \le 9$ , $y \ge 0$ , $x - y \ge 0$ (i.e. $y \le x$ ), $x + y \le 14$

Corner points are formed where two boundary lines intersect inside the feasible region.

$x = 3$ meets $y = 0$

Corner point $= (3,\; 0)$

$x = 9$ meets $y = 0$

Corner point $= (9,\; 0)$

$x = 9$ meets $x + y = 14$

$y = 14 - 9 = 5$

Corner point $= (9,\; 5)$

$x + y = 14$ meets $y = x$

$x + x = 14$

$2x = 14$

$x = 7,\; y = 7$

Corner point $= (7,\; 7)$

$x = 3$ meets $y = x$

$y = 3$

Corner point $= (3,\; 3)$

Checking option 1: $(0, 0)$ fails $x \ge 3$ — not in feasible region. ❌

Checking option 2: $(14, 0)$ fails $x \le 9$ — not in feasible region. ❌

Checking option 3: $(7, 7)$ and $(3, 3)$ — both are valid corner points. ✅

Checking option 4: At $(3, 6)$ , $x - y = 3 - 6 = -3 < 0$ — fails $x - y \ge 0$ . ❌

The answer is Option 3 — $(7, 7)$ and $(3, 3)$ .

2025: 2 June Shift 1

Linear inequalities corresponding to the shaded feasible region OABCO in the given figure are

2025: 14 May Shift 2

Consider the linear programming problem(LPP):

Minimize $Z = x + y$

$x + 2y \leq 4,$

$3x + y \geq 3,$

$4x + 3y \geq 6,$

$x, y \geq 0.$

Which of the following is correct for the above linear programming problem (LPP):

(A) The LPP has a bounded feasible region.

(B) The LPP has a unique optimal solution.

(D) The corner points of the feasible region are (3/2, 0), (3/5, 6/5), (2/5, 6/5) and (4, 0)

Choose the correct answer from the options given below:

2025: 14 May Shift 2

If the objective function $Z = px + qy, p > 0, q > 0$ of a linear programming problem attains its optimal value at the points (4, 7) and (5, 5) and $pq = 50$ then

2026: 30 May Shift 2

Consider the linear programming problem (LPP):

Max Z= 4x + 3y

subject to the constraints:

$x\le 8, y\le 4, x\ge 0, y\ge 0$ . At what coordinates will the objective function have optimal solution?

2025: 3 June Shift 1

If the feasible region of an LPP is bounded and the corresponding objective function is $z = 5x - 9y$ , then the objective function attains:

2026: 19 May Shift 1

The shaded unbounded area of an LPP is the result of constraints:

A linear programming problem is as follows: Minimize z=2x+3yz = 2x + 3yz=2x+3y Subject to the constraints x≥3,x≤9,y≥0,x−y≥0,x+y≤14x \ge 3, x \le 9, y \ge 0, x - y \ge 0, x + y \le 14x≥3,x≤9,y≥0,x−y≥0,x+y≤14. The feasible region has 5 corner points including

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

A linear programming problem is as follows:

Minimize $z = 2x + 3y$

Subject to the constraints $x \ge 3, x \le 9, y \ge 0, x - y \ge 0, x + y \le 14$ . The feasible region has 5 corner points including