Maximum value of Z equals to 40x + 50y subject to constraints $3x + y \leq 9$, $x + 2y \leq 8$, $x, y \geq 0$ occurs at

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 ?

Objective function $Z = 200x + 500y$, subject to constraint, $x + 2y \geq 10, 3x + 4y \leq 24$, $x \geq 0, y \geq 0$ - (iii), the minimum value of Z is :

The Solution set of the inequality three $3x + 4y \leq 12$ 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

Match List I with List II

Choose the correct answer from the options given below:

Corner points of the feasible region for an LPP are : (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let $z = 4x + 6y$ be the objective function. Then, Max z $-$ Min z is equal to :