MHT CET PYQs for Linear Programming Problem with Solutions: Practice MHT CET Previous Year Questions

1.

The LPP maximize \(z = 2x+5y\) subject to \(x+3y\leq 6\), \(2x+6y\leq 18\), \(x\geq 0\), \(y\geq 0\) has

• Unique solution
• Infinite solutions
• No solution
• Unbounded feasible region

2.

In the following figure, the shaded region represents the system of constraints:

• \(2x+y\leq 12,x+2y\leq 12,x+1.25y\geq 5,x\leq 0,y\geq 0\)
• \(2x+y\leq 12,x+2y\leq 12,x+1.25y\geq 5,x\geq 0,y\leq 0\)
• \(2x+y\leq 12,x+2y\leq 12,x+1.25y\leq 5,x\geq 0,y\geq 0\)
• \(2x+y\leq 12,x+2y\leq 12,x+1.25y\geq 5,x\geq 0,y\geq 0\)

3.

For the linear programming problem, \(x+2y\leq 10, 3x+y\leq 12, x,y\geq 0\), the maximum value of \(z = 5x+10y\) occurs at every point on the line segment joining the points..

• \((0,0)\) and \((4,0)\)
• \((0,0)\) and \((0,5)\)
• \((4,0)\) and \((\frac{14}{5},\frac{18}{5})\)
• \((0,5)\) and \((\frac{14}{5},\frac{18}{5})\)

4.

The feasible region represented by the constraints \(y-2x\leq 4,x+y\geq 5,x\leq 4,y\geq 2,x,y\geq 0\) is ...........

• a convex bounded region with 4 corner points
• an unbounded region
• a convex bounded region with 5 corner points
• no feasible region

5.

The minimum value of \(Z = 3x+y\), subject to the constraints \(2x+3y\leq 6,x+y\geq 1,x\geq 0,y\geq 0\) is....

• \(5\)
• \(2\)
• \(1\)
• \(9\)

6.

The difference between the maximum value and minimum value of the objective function \(z = 3x+5y\) of a linear programming problem subject to constraints \(5x+10y\leq 50\), \(x+y\geq 1\), \(y\leq 4\) and \(x\geq 0,y\geq 0\) is \(3λ\). Then the value of \(λ\) is

• \(3\).
• \(6\).
• \(9\).
• \(27\).

7.

The maximum value of \(Z = 4x+5y\), subject to the constraints \(3x+y\leq 15,3x+4y\leq 24,x\geq 0,y\geq 0\) is

• \(31\)
• \(30\)
• \(42\)
• \(47\)

8.

In L.P.P., the corner points of the feasible region for the constraints \(3x-y\geq 6,x\leq 3,y\leq 2,y\geq 0,x\geq 0\) are .....

• \((3,2),(3,0),(2,0)\)
• \((\frac{8}{3},2),(3,2),(3,0),(2,0)\)
• \((0,0),(2,0),(\frac{8}{3},2),(0,2)\)
• \((3,2),(0,3),(0,2)\)

9.

The shaded region in the provided graph represents the solution set for which of the following systems of linear inequalities?

• \(2x+y\geq 2, x-y\geq 1, x+2y\leq 8, x\geq 0, y\geq 0\)
• \(x+2y\geq 2, x-y\geq 1, x+2y\leq 8, x\geq 0, y\geq 0\)
• \(2x+y\geq 2, x-y\leq 1, x+2y\leq 8, x\geq 0, y\geq 0\)
• \(2x+y\geq 2, x-y\leq 1, 2x+y\leq 8, x\geq 0, y\geq 0\)

10.

An airplane can carry a maximum of \(250\) passengers. A profit of Rs \(1500\) is made on each executive class ticket and a profit of Rs \(900\) is made on each economy class ticket. The airline reserves at least \(30\) seats for executive class. However at least \(4\) times as many passengers prefer to travel by economy class than by executive class. Let \(x_1\) be the number of passengers of executive class and \(x_2\) be the number of passengers of economy class. Formulate the LPP in order to maximize the profit for the airline...

• Maximize \(z = 1500x_1+900x_2\) subject to \(x_1+x_2\leq 250\), \(x_1\leq 30\), \(x_2\leq 4x_1\), \(x_1\geq 0,x_2\geq 0\).
• Minimize \(z = 150x_1+90x_2\) subject to \(x_1+x_2\leq 250\), \(x_1\geq 30\), \(x_2\geq 4x_1\), \(x_1\geq 0,x_2\geq 0\).
• Minimize \(z = 1500x_1+900x_2\) subject to \(x_1+x_2\leq 250\), \(x_1\geq 30\), \(x_2\geq 4x_1\), \(x_1\geq 0,x_2\geq 0\).
• Maximize \(z = 1500x_1+900x_2\) subject to \(x_1+x_2\leq 250\), \(x_1\geq 30\), \(x_2\geq 4x_1\), \(x_1\geq 0,x_2\geq 0\).

11.

The region satisfying the inequalities \(y-x\geq 2, x+y\leq 5, x\geq 0\) and \(y\geq 0\) is

12.

In L.P.P., the maximum value of objective function $Z = 6x + 3y$ subject to $x + y \leq 5, x + 2y \geq 4, 4x + y \leq 12, x, y \geq 0$ is \dots

• 132/7
  
• 22
  
• 15
  
• 122/7

13.

The solution for minimizing the function $z = x + y$ under an L.P.P. with constraints $x + y \ge 2$, $x + 2y \le 8$, $y \le 3$, $x, y \ge 0$ is ______.

• at the point (0, 3)
  
• at the point (8, 0)
  
• at infinite number of points but bounded set
  
• at unbounded set
  

14.

The point at which the maximum value of \(x+y\) subject to constraints \(x+2y\leq 70\) and \(2x+y\leq 95,x\geq 0,y\geq 0\) is.

• \((47.5,0)\)
• \((0,95)\)
• \((0,35)\)
• \((40,15)\)

15.

The minimum value of \(z = 3x+5y\), subject to constraints \(x\leq 80\), \(y\geq 60\), \(x+y\leq 200\) & \(x,y\geq 0\) occurs at the point...

• \((0,200)\)
• \((60,0)\)
• \((0,60)\)
• \((80,60)\)