A LPP $max\,Z = 3x + 8y$ subjected to the constraints $2x + y \le 10$, $x + 3y \le 15$, $x,y \ge 0$, then $max\,Z$ is

The minimum cost of the mixture is-

Which one of the following set of constraints does the given shaded region represent?

The corner points of the feasible region for an L.P.P. are $(0, 10)$, $(5, 5)$, $(5, 15)$ and $(0, 30)$. If the objective function is $Z = \alpha x + \beta y$, where $\alpha, \beta > 0$, find the condition on $\alpha$ and $\beta$ so that the maximum of $Z$ occurs at both the corner points $(5, 15)$ and $(0, 30)$.

The corner points of the feasible region determined by a system of linear constraints are $(0, 0)$, $(0, 40)$, $(20, 40)$, $(60, 20)$, $(60, 0)$. If the objective function is $z = 4x + 3y$, then which one of the following is true?

While solving an LPP, the corner points of a bounded feasible region were found to be (0,0), (1, 9), (3, 7), (4, 5.5) and (10, 0). The objective function $Z = 4x + y$ will maximise at:

If a person rides his motorbike $x$ km at 30 km per hour, he has to spend ₹ 3 per kilometer on petrol. If he rides $y$ km at a faster speed of 40 km per hour, the petrol cost increases to ₹ 4 per kilometer. If he has ₹ 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour, then linear programming problem (LPP) formulation is: