List of top Mathematics Questions on Linear Programming

The feasible region is bounded by the inequalities: \[ 3x + y \geq 90, \quad x + 4y \geq 100, \quad 2x + y \leq 180, \quad x, y \geq 0 \] If the objective function is $ Z = px + qy $ and $ Z $ is maximized at points $ (6, 18) $ and $ (0, 30) $, then the relationship between $ p $ and $ q $ is:
For any Linear Programming Problem (LPP), choose the correct statement:
A. There exists only finite number of basic feasible solutions to LPP
B. Any convex combination of k - different optimum solution to a LPP is again an optimum solution to the problem
C. If a LPP has feasible solution, then it also has a basic feasible solution
D. A basic solution to AX = b is degenerate if one or more of the basic variables vanish
For the given linear programming problem,
Minimum Z = 6x + 10y
subject to the constraints
\( x \ge 6 \); \( y \ge 2 \); \( 2x+y \ge 10 \); \( x,y \ge 0 \),
the redundant constraints are:
Maximize \( Z = 2x+3y \), subject to the constraints:
\( x+y \le 2 \)
\( 2x+y \le 3 \)
\( x,y \ge 0 \)
Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize Z = 5x + 2y
subject to the following constraints
3x + 5y \(\le\) 15,
5x + 2y \(\le\) 10,
x \(\ge\) 0, y \(\ge\) 0.
(A) The LPP has a unique optimal solution at (2, 0) only.
(B) The feasible region is bounded with corner points (0, 0), (2, 0), (20/19, 45/19) and (0, 3).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:
Which of the following is NOT a basic requirement of the linear programming problem (LPP)?
Which one of the following set of constraints does the given shaded region represent?
The corner points of the feasible region of the LPP: Minimize \( Z = -50x + 20y \) subject to \( 2x - y \geq -5 \), \( 3x + y \geq 3 \), \( 2x - 3y \leq 12 \), and \( x, y \geq 0 \) are:
The corner points of the feasible region associated with the LPP: Maximise Z = px + qy, p, q > 0 subject to 2x + y $\le$ 10, x + 3y $\le$ 15, x,y $\ge$ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then
Consider the LPP: Minimize Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0. The optimal feasible solution occurs at
Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize Z = 5x + 2y
subject to the following constraints
3x + 5y \(\le\) 15,
5x + 2y \(\le\) 10,
x \(\ge\) 0, y \(\ge\) 0.
(A) The LPP has a unique optimal solution at (2, 0) only.
(B) The feasible region is bounded with corner points (0, 0), (2, 0), (20/19, 45/19) and (0, 3).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:
Which of the following is NOT a basic requirement of the linear programming problem (LPP)?
The corner points of the feasible region of the LPP: Minimize \( Z = -50x + 20y \) subject to \( 2x - y \geq -5 \), \( 3x + y \geq 3 \), \( 2x - 3y \leq 12 \), and \( x, y \geq 0 \) are:
Which one of the following set of constraints does the given shaded region represent?
The corner points of the feasible region associated with the LPP: Maximise Z = px + qy, p, q > 0 subject to 2x + y $\le$ 10, x + 3y $\le$ 15, x,y $\ge$ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). If optimum value occurs at both (3, 4) and (0, 5), then
Consider the LPP: Minimize Z = x + 2y subject to 2x + y $\ge$ 3, x + 2y $\ge$ 6, x, y $\ge$ 0. The optimal feasible solution occurs at

Solve the following LPP graphically: Maximize: \[ Z = 2x + 3y \] Subject to: \[ \begin{aligned} x + 4y &\leq 8 \quad \text{(1)} \\ 2x + 3y &\leq 12 \quad \text{(2)} \\ 3x + y &\leq 9 \quad \text{(3)} \\ x &\geq 0,\quad y \geq 0 \quad \text{(non-negativity constraints)} \end{aligned} \]

In an LPP, corner points of the feasible region determined by the system of linear constraints are \((1,1), (3,0), (0,3)\). If \(Z = ax + by\), where \(a>0, b>0\) is to be minimized, the condition on \(a\) and \(b\) so that the minimum of \(Z\) occurs at \((3, 0)\) and \((1, 1)\) will be:
The maximum value of \(Z = 3x + 4y\) subject to the constraints \(x + y \leq 1\), \(x \geq 0\), \(y \geq 0\) is:
Corner points of a feasible bounded region are \((0, 10)\), \((4, 2)\), \((3, 7)\) and \((10, 6)\). Maximum value 50 of objective function \(z = ax + by\) occurs at two points \((0, 10)\) and \((10, 6)\). The value of \(a\) and \(b\) are:
The vertices of a closed convex polygon representing the feasible region of the LPP with objective function \(z = 5x + 3y\) are \((0,0)\), \((3,1)\), \((1,3)\) and \((0,2)\). The maximum value of \(z\) is:

A person wants to invest at least ₹20,000 in plan A and ₹30,000 in plan B. The return rates are 9% and 10% respectively. He wants the total investment to be ₹80,000 and investment in A should not exceed investment in B. Which of the following is the correct LPP model (maximize return $ Z $)?

The feasible region is bounded by the inequalities: \[ 3x + y \geq 90, \quad x + 4y \geq 100, \quad 2x + y \leq 180, \quad x, y \geq 0 \] If the objective function is $ Z = px + qy $ and $ Z $ is maximized at points $ (6, 18) $ and $ (0, 30) $, then the relationship between $ p $ and $ q $ is:
A person wants to invest at least ₹20,000 in plan A and \₹30,000 in plan B. The return rates are 9% and 10% respectively. He wants the total investment to be ₹80,000 and investment in A should not exceed investment in B. Which of the following is the correct LPP model (maximize return $ Z $)?

Find the minimum value of  ( z = x + 3y ) under the following constraints: 

• x + y ≤ 8
• 3x + 5y ≥ 15
• x ≥ 0, y ≥ 0