The corner points of the bounded feasible region determined by a set of constraints in an LPP are $P(0, 5)$, $Q(3, 5)$, $R(5, 0)$ and $S(4, 1)$. If the objective function is $z = ax + 2by$, where, $a, b > 0$, then the condition on $a$ and $b$ such that the maximum value of $z$ occurs at $Q$ and $S$ is

Which one of the following inequalities is redundant for the shaded feasible region (ABCDA) shown below?

A company makes two types of cakes: type A and type B. it costs ₹ 360 to make a type A cake and ₹ 120 to make a type B cake. The company can make atmost 300 cakes and spend atmost ₹ 72,000 a day, the number of cakes of type B ($y$) cannot exceed the number of type A ($x$) cakes by more than 200.

The company makes a profit of ₹ 200 on each type A cake and ₹ 50 on each type B cake. A LPP to maximize the profit (₹) is

The objective function of an LPP is $z = ax + \beta y, (a, \beta > 0)$ in that has to be maximized/minimized subject to constraints

$x + y \leq 2$, $x \geq 0$, $y \geq 0$. Then max (z) $-$ min (z) is equal to

Which one of the following set of constraints represents the shaded region given below?

The feasible region of an LPP is a bounded region by vertices (4, 18), (6, 12), (40, 0) and (15, 0). Then the point (15, 15) lies in the

A. open half plane of $x+2y<40$.

B. closed half plane of $3x+y\ge 30$.

C. closed half plane of $4x+3y\ge 60$.

D. feasible region of the given LPP.

Choose the correct answer from the options given below:

Linear inequalities corresponding to the shaded feasible region OABCO in the given figure are