If the minimum value of an objective function $Z=a x+$ by occurs at two points $(3,4)$ and $(4,3)$ then
- A$a+b=0$
- B$a=b$
- C$3 a=b$
- D$a=3 b$
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Linear Programming question types
243 questions across 3 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
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Sample Questions
Linear Programming questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
For the following LPP, maximise $Z=3 x+4 y$ subject to constraints $x-y \geq-1, x \leq 3, x \geq 0, y \geq 0$ the maximum value is
- A$0$
- B4
- C25
- D30
The feasible region of an LPP is given in the following figure
Then, the constraints of the LPP are $x \geq 0, y \geq 0$ and
Then, the constraints of the LPP are $x \geq 0, y \geq 0$ and
- A$2 x+y \leq 52$ and $x+2 y \leq 76$
- B$2 x+y \leq 104$ and $x+2 y \leq 76$
- C$x+2 y \leq 104$ and $2 x+y \leq 76$
- D$x+2 y \leq 104$ and $2 x+y \leq 38$
Based on the given shaded region as the feasible region in the graph, at which point(s) is the objective function $Z=3 x+9 y$ maximum?
- APoint $B$
- BPoint $C$
- CPoint $D$
- Devery point on the line segment $C D$
In a linear programming problem, the constraints on the decision variables $x$ and $y$ are $x-3 y \geq 0, y \geq 0$, $0 \leq x \leq 3$. The feasible region
- Ais not in the first quadrant
- Bis bounded in the first quadrant
- Cis unbounded in the first quadrant
- Ddoes not exist
Solve the Linear Programming Problem graphically:
Minimize Z = -3x + 4y subject to $x + 2y \leq 8, \ 3x + 2y \leq 12, \ x \geq 0, \ y \geq 0.$
View full solution →Minimize Z = -3x + 4y subject to $x + 2y \leq 8, \ 3x + 2y \leq 12, \ x \geq 0, \ y \geq 0.$
Show that the minimum of Z occurs at more than two points.
Maximize Z = x + y, subject to $x - y \leq - 1, - x + y \leq 0, \ x, \ y \geq 0$.
View full solution →Maximize Z = x + y, subject to $x - y \leq - 1, - x + y \leq 0, \ x, \ y \geq 0$.
Solve the Linear Programming Problem graphically:
Maximise Z = 3x + 4y subject to the constraints: $x + y \le4, \ x \geq 0, \ y \geq 0$
View full solution →Maximise Z = 3x + 4y subject to the constraints: $x + y \le4, \ x \geq 0, \ y \geq 0$
Solve the following linear programming problem graphically:
Minimise Z = 200x + 500y subject to the constraints:
$x + 2 y \geq 10$
$3 x + 4 y \leq 24$
$x \geq 0 , y \geq 0$
View full solution →Minimise Z = 200x + 500y subject to the constraints:
$x + 2 y \geq 10$
$3 x + 4 y \leq 24$
$x \geq 0 , y \geq 0$
Solve the following linear programming problem graphically:
Maximise Z = 4x + y subject to the constraints:
x + y $\le$ 50
3x + y $\le$ 90
x $\ge$ 0, y $\ge$ 0
View full solution →Maximise Z = 4x + y subject to the constraints:
x + y $\le$ 50
3x + y $\le$ 90
x $\ge$ 0, y $\ge$ 0
Show that the minimum of Z occurs at more than two points.
Maximize Z = -x + 2y subject to the constraints: $x \geq 3,x + y \geq 5,x + 2y \geq 6,y \geq 0$.
View full solution →Maximize Z = -x + 2y subject to the constraints: $x \geq 3,x + y \geq 5,x + 2y \geq 6,y \geq 0$.
Show that the minimum of Z occurs at more than two points.
Minimise and Maximise Z = x + 2y subject to $x + 2 y \geq 100,2 x - y \leq 0,2 x + y \leq 200$; $x , \ y \geq 0$.
View full solution →Minimise and Maximise Z = x + 2y subject to $x + 2 y \geq 100,2 x - y \leq 0,2 x + y \leq 200$; $x , \ y \geq 0$.
Show that the minimum of Z occurs at more than two points.
Minimize and Maximize Z = 5x + 10y subject to $x + 2y \leq 120, \ x + y \geq 60$, $x - 2y \geq 0, \ x, \ y \geq 0$.
View full solution →Minimize and Maximize Z = 5x + 10y subject to $x + 2y \leq 120, \ x + y \geq 60$, $x - 2y \geq 0, \ x, \ y \geq 0$.
Solve the Linear Programming Problem graphically:
Minimise Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0.
View full solution →Minimise Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0.
Solve the Linear Programming Problem graphically:
Maximize Z = 3x + 2y subject to $x + 2y \leq 10,3x + y \leq 15,x,y \geq0$
View full solution →Maximize Z = 3x + 2y subject to $x + 2y \leq 10,3x + y \leq 15,x,y \geq0$
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