Question:
In a linear programming problem, the linear function which has to be maximized or minimized is called
In a linear programming problem, the linear function which has to be maximized or minimized is called
Show Hint
The objective function represents quantities like profit, cost, or distance.
Non-negativity restrictions (\( x, y \geq 0 \)) are almost always present in standard LPPs.
Non-negativity restrictions (\( x, y \geq 0 \)) are almost always present in standard LPPs.
Updated On: Sep 10, 2026
- a feasible function
- an objective function
- an optimal function
- a constraint
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
• Linear Programming Problem (LPP) involves optimizing a linear function subject to linear constraints.
• Constraints are the system of linear inequalities or equations.
• The feasible region is the set of all points that satisfy all constraints.
Step 1: Define the function being optimized
In any optimization problem, the goal is to find the maximum or minimum value of a specific function.
This specific function, usually denoted by \( Z = ax + by \), is defined as the objective function.
Step 2: Distinguish between the different LPP components
Constraints are the conditions that limit the variables (e.g., \( x + y \leq 5 \)).
The feasible function refers to the values within the valid region.
The optimal value is the actual max/min numerical result obtained at the corner points.
Step 3: Conclusion
Therefore, the function itself is called the objective function.
• Linear Programming Problem (LPP) involves optimizing a linear function subject to linear constraints.
• Constraints are the system of linear inequalities or equations.
• The feasible region is the set of all points that satisfy all constraints.
Step 1: Define the function being optimized
In any optimization problem, the goal is to find the maximum or minimum value of a specific function.
This specific function, usually denoted by \( Z = ax + by \), is defined as the objective function.
Step 2: Distinguish between the different LPP components
Constraints are the conditions that limit the variables (e.g., \( x + y \leq 5 \)).
The feasible function refers to the values within the valid region.
The optimal value is the actual max/min numerical result obtained at the corner points.
Step 3: Conclusion
Therefore, the function itself is called the objective function.
Was this answer helpful?
0
0
Top CBSE CLASS XII Mathematics Questions
- 2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
- A committee of 11 members is to be formed from 8 males and 5 females. Let m denotes the number of ways of selecting committee having atleast 6 males and n denotes the number of ways of selecting atleast 3 females then
Determine whether each of the following relations are reflexive, symmetric, and transitive.
- Relation R in the set A={1,2,3,...13,14} defined as R={(x,y): 3x-y=0}.
- Relation R in the set of N natural numbers defined as R={(x,y): y=x+5 and x<4}.
- Relation R in the set A={1,2,3,4,5,6} defined as R={(x,y): y is divisible by x}.
- Relation R in the set of Z integers defined as R={(x,y): x-y is an integer}
- Relation R in the set of human beings in a town at a particular time given by
- R={(x,y): x and y work at same place}
- R={(x,y): x and y live in the same locality}
- R={(x,y): x is exactly 7 am taller that y}
- R={(x,y): x is wife of y}
- R={(x,y):x is father of y}
Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
View More Questions
Top CBSE CLASS XII Linear Programming Questions
- 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:
Solve the following LPP graphically: Maximize: \[ Z = 2x + 3y \] Subject to: \[ \begin{aligned} x + 4y &\leq 8 \quad \text{(1)} \\ 2x + 3y &\leq 12 \quad \text{(2)} \\ 3x + y &\leq 9 \quad \text{(3)} \\ x &\geq 0,\quad y \geq 0 \quad \text{(non-negativity constraints)} \end{aligned} \]
- The feasible region of a linear programming problem with objective function \( Z = 5x + 7y \) is shown below :
- The degree of an objective function of a linear programming problem is
View More Questions
Top CBSE CLASS XII Questions
- 2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
- A boy of mass 50 kg is standing at one end of a, boat of length 9 m and mass 400 kg. He runs to the other, end. The distance through which the centre of mass of the boat boy system moves is
- A capillary tube of radius r is dipped inside a large vessel of water. The mass of water raised above water level is M. If the radius of capillary is doubled, the mass of water inside capillary will be
- A circular disc is rotating about its own axis. An external opposing torque 0.02 Nm is applied on the disc by which it comes rest in 5 seconds. The initial angular momentum of disc is
- A circular disc is rotating about its own axis at uniform angular velocity \(\omega.\) The disc is subjected to uniform angular retardation by which its angular velocity is decreased to \(\frac {\omega}{2}\) during 120 rotations. The number of rotations further made by it before coming to rest is
View More Questions