Consider the following statements:Statement ( | vedclass

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(A) Both Statement $(I)$ and Statement $(II)$ are true in a Linear Programming Problem $(LPP)$:Statement $(I)$:The objective function in an $LPP$ is a

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Statement $(I)$ is true,Statement $(II)$ is true

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(A) Both Statement $(I)$ and Statement $(II)$ are true in a Linear Programming Problem $(LPP)$:Statement $(I)$:The objective function in an $LPP$ is always linear,meaning it can be expressed as a linear equation with the variables raised to the power of $1$.Statement $(II)$:The linear inequalities that restrict the variables in an $LPP$ are called constraints.Explanation:In a linear programming problem,you are trying to optimize (maximize or minimize) an objective function (a linear equation) while adhering to certain constraints (linear inequalities) that limit the possible values of the variables.

Column	Value
$A$. Maximum of $z$	$300$
$B$. Constant value	$325$

Consider the following statements:
Statement $(I)$: In a $LPP$,the objective function is always linear.
Statement $(II)$: In a $LPP$,the linear inequalities on variables are called constraints.
Which of the following is correct?

Similar Questions

Maximize $Z=3x+4y$,subject to the constraints: $x+y \leq 1, x \geq 0, y \geq 0$.

The corner points of the feasible region determined by the system of linear constraints are $(0,0), (0,40), (20,40), (60,20), (60,0)$. The objective function is $z=4x+3y$. Compare the quantity in Column $A$ and Column $B$.

Column Value

$A$. Maximum of $z$ $300$

$B$. Constant value $325$

Solve the Linear Programming Problem graphically:
Maximise $Z = 5x + 3y$
subject to the constraints:
$3x + 5y \leq 15$
$5x + 2y \leq 10$
$x \geq 0, y \geq 0$

Determine graphically the minimum value of the objective function
$Z = -50x + 20y$ .....$(1)$
subject to the constraints:
${2x - y \geqslant -5}$ .....$(2)$
${3x + y \geqslant 3}$ .....$(3)$
${2x - 3y \leqslant 12}$ .....$(4)$
${x \geqslant 0, y \geqslant 0}$ .....$(5)$

Show that the minimum of $Z$ occurs at more than two points.
Minimise and Maximise $Z = x + 2y$
subject to $x + 2y \geq 100, 2x - y \leq 0, 2x + y \leq 200; x, y \geq 0$.

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Consider the following statements:Statement $(I)$: In a $LPP$,the objective function is always linear.Statement $(II)$: In a $LPP$,the linear inequalities on variables are called constraints.Which of the following is correct?