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

Let $Z=ux+vy$, $u,v>0$ be the objective function of a linear programming problem. Then the condition on $u$ and $v$ so that the maximum of $Z$ occurs at both points $(3,4)$ and $(0,5)$ is :

Consider the linear programming problem (LPP):

Max Z= 4x + 3y

subject to the constraints:

$x\le 8, y\le 4, x\ge 0, y\ge 0$. At what coordinates will the objective function have optimal solution?

Which one of the following represents the correct feasible region determined by the following constraints

$x - y \geq 5$, $5x - 5y \leq 16$

Consider a L.P.P, Maximize $Z = 3x + 5y$ subject to constraints $2x + 6y ≤ 6$, $x - y ≥ 0$, $x ≥ 0$, $y ≥ 0$. Then which of the following are true?

(A) The feasible region of L.P.P is bounded region

(B) The corner points of the feasible region are (0, 0), (2, 2), (0, 1)

(C) Maximum value of Z is 9

(D) Point (1, 3) lies in the feasible region

Choose the correct answer from the options given below:

In a Linear Programming problem, the objective function is always :

The maximum value of $z$ for the linear programing problem maximize $z = x + y$ subject to the constraints $x + 4y \leq 8, 2x + 3y \leq 12, 3x + y \leq 9, x \geq 0, y \geq 0$ is: