In a LPP, Let R be the feasible region, then which of the following are TRUE?

A. If R is bounded, then the objective function Z has both a maximum and minimum value on R.

B. If R is unbounded, then the objective function Z may or may not have a maximum or minimum value.

C. If a optimal solution exists. It must occur at atleast one corner point of R.

D. If R is bounded, then maximum value will exist but minimum may or may not exist for an objective function Z.

Choose the correct answer from the options given below:

A company makes two types of cakes: type A and type B. it costs ₹ 360 to make a type A cake and ₹ 120 to make a type B cake. The company can make atmost 300 cakes and spend atmost ₹ 72,000 a day, the number of cakes of type B ($y$) cannot exceed the number of type A ($x$) cakes by more than 200.

The company makes a profit of ₹ 200 on each type A cake and ₹ 50 on each type B cake. A LPP to maximize the profit (₹) is

The programming problem

Max $Z = 2x + 3y$ subject to the conditions $0 \leq x \leq 3, 0 \leq y \leq 4$ is :

The feasible region for an LPP is shown by shaded region in the figure. Then the minimum value of Z = 11x + 7y is

Linear inequalities corresponding to the shaded feasible region OABCO in the given figure are

For the LPP,

$Z=20x+10y$

Subject to

$x+2y\le 40$

$3x+y\ge 30$

$4x+3y\ge 60$

$x,y\ge 0$

Match List-I with List-II

List-I	List-II
(A) $Max.Z$	(I) 180
(B) $Min.Z$	(II) 320
(C) $Max.Z - 2\,Min.Z$	(III) 240
(D) If $Min.Z$ is attained at $(\alpha,\beta)$, then $\alpha^2+\beta^2$ is	(IV) 800

Choose the correct answer from the options given below:

As per the below-mentioned graph of shaded bounded feasible region of the LPP, the maximum value of the objective function $z = 2x + y$ is