10 Question MCQ (including Assertion)

The feasible solution for a LPP is shown in Fig. 12.12. Let \(Z=3 x-\) 4 y be the objective function. (Maximum value of \(\mathrm{Z}+\) Minimum value of Z) is equal to

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 \(\mathrm{Z}=4 \mathrm{x}+3 \mathrm{y}\).
Compare the quantity in Column A and Column B

The region represented by the system of inequations \(3 \mathrm{x}+\mathrm{y} \geq 3\), \(2 \mathrm{x}-\mathrm{y} \geq-5, \mathrm{x}, \mathrm{y} \geq 0\) is :

Corner points of the feasible region determined by the system of linear constraints are \((0,3),(1,1)\) and \((3,0)\). Let \(Z=p x+q y\), where \(p, q>0\). Condition on \(p\) and \(q\) so that the minimum of \(Z\) occurs at \((3,0)\) and \((1,1)\) is

Assertion (A) : Every point of the feasible region of a Linear Programming Problem is an optimal solution.
Reason (R) : The optimal solution for a Linear Programming Problem exists only at one or more corner point(s) of the feasible region.

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let \(\mathrm{Z}=\mathrm{px}+\) qy, where \(\mathrm{p}, \mathrm{q}>0\). Condition on p and q so that the maximum of Z occurs at both the points \((15,15)\) and \((0,20)\) is

Feasible region (shaded) for a LPP is shown in the Fig. 12.6.
Minimum of \(\mathrm{Z}=4 \mathrm{x}+3 \mathrm{y}\) occurs at the point

Corner points of the feasible region for an LPP are \((0,2),(3,0),(6\), \(0),(6,8)\) and \((0,5)\).

Let \(F=4 x+6 y\) be the objective function.
Maximum of \(\mathrm{F}-\) Minimum of \(\mathrm{F}=\)

Corner points of the feasible region for an LPP are \((0,2),(3,0),(6,0)\), \((6,8)\) and \((0,5)\).

Let \(F=4 x+6 y\) be the objective function.
The Minimum value of F occurs at