The corner points of feasible region determined by the following system of linear inequalities $2x + y \leq 10, x + 3y \leq 15, x \geq 0, y \geq 0$ are $(0,0), (5,0), (3,4)$ and $(0,5)$, then the relation between p and Q so that minimum of Z occurs both points $(3,4)$ and $(0,5)$ is :

The bounded feasible region of an LPP is shown in the diagram given below.

The objective function $z=3x+10y$ attains optimum values at :

A. Point (0,0)

B. Point (0,4)

C. Point (6,3)

D. Point (5,6)

Choose the correct answer from the options given below:

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let $Z = ax + by$, where a, b > 0. Condition on a and b so that the maximizing value of Z occurs at both the points (15, 15) and (0, 20) is:

Objective function of a LPP represent

Which constraints correctly represent the situation 'mixture of x and y must be at least 8 units' ?

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 ?

If the objective function $z=10(x-7y+190)$ and the corner points of the bounded feasible region are A(0,4), B(0,5), C(3,5), D(5,3), E(5,0), F(4,0), then the minimum value of z will be: