The feasible region for an LPP is shown in the figure given below: If objective is maximizing $Z = 22x + 18y$ find $(x, y)$ for the optimal $Z$.

The maximum value of $Z = 3x + y$ subject to the constraints $x + y \leq 30, 2x + y \leq 40, x, y \geq 0$ is

The minimum value of $Z = 30x + 10y$ subject to the constraints $x + 2y \leq 30, 3x + y \geq 30, 4x + 3y \geq 60, x, y \geq 0$ is

In an LPP if the objective function $z = ax + by$ has same maximum value on two corner points of the feasible region, then the number of points at which maximum value of $z$ occurs is :

Given a linear programming problem,

Max $Z = 22x + 18y$, Subject to constraints

$x + y \leq 20, 360x + 240y \leq 5760, x \geq 0, y \geq 0$. Its corner points are :

The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$, are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is :

Every gram of wheat provides 0.15 g of proteins and 0.24 g of carbo hydrates. The corresponding values of proteins and carbo hydrate of rice are 0.05g and 0.48g respectively. Wheat costs ₹40 per kg and rice costs ₹60 per kg. The minimum daily requirements of proteins and carbohydrates for an average child are 50g and 200 g respectively. Which of the following options describes the LPP to minimize the total cost of wheat and rice that provide minimum daily requirements of proteins and carbohydrates ?