Match List - I with List - II.

List - I	List - II
(A) The common region determined by all the linear constraints of a L.P.P. is called	(I) corner point
(B) A point in the feasible region which is the intersection of two boundary lines is called,	(II) non-negative
(C) The feasible region for an LPP is always a	(III) feasible region
(D) The constraints $x, y \geq 0$ describes that the variables involved in a LPP are	(IV) convex polygon

Choose the correct answer from the options given below :

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 feasible reason for the constraints $x \geq 0$, $x + y \leq 1$ and $x - y \leq 1$, is situated in :

(A) I and II quadrant only

(B) I Quadrant

(C) II and IV Quadrant

(D) IV Quadrant

(E) I , II , III and IV Quadrant

Choose the correct answer from the option 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:

Match List I with List II

Choose the correct answer from the options given below:

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 ?

The maximum value of $Z = 3x + 4y$ subjected to the constraints $3x + 7y \leq 21$, $5x + 2y \leq 10$; $x, y \geq 0$ is :