The minimum value of $z = 3x + 6y$ subject to the constraints $2x + 3y \leq 180$, $x + y \geq 60$, $x \geq 3y$, $x \geq 0$, $y \geq 0$ is :

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 :

A company produces two types of belts A & B with a profit of Rs 2 and Rs 1.50 respectively. Belt of type A needs twice as much time to make as belt type B . The company can produce at the most 1000 belts of type B per day . Material for 800 belts is available per day . At the most , 400 buckles for belt type A and 700 for belts type B are available . Then the appropriate LPP 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 :

The corner point of the feasible region determined by a set of linear constraints are : (0,0) , (0,4), (2,5) , (6,3) and (6,0) then which of the following point lie in the feasible region ?

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 $Z$.

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 ?