The maximum value of $z=3x+4y$,subject to the constraints $x+y \leq 40$,$x+2y \leq 60$ and $x, y \geq 0$ is

In the following figure, the shaded region represents the system of constraints:

The difference between the maximum value and minimum value of the objective function $z = 3x + 5y$ subject to the constraints $x + 3y \leqslant 60$,$x + y \geqslant 10$,$x - y = 0$,and $x, y \geqslant 0$ is:

$A$ factory makes tennis rackets and cricket bats. $A$ tennis racket takes $1.5\, \text{hours}$ of machine time and $3\, \text{hours}$ of craftsman's time in its making, while a cricket bat takes $3\, \text{hours}$ of machine time and $1\, \text{hour}$ of craftsman's time. In a day, the factory has the availability of not more than $42\, \text{hours}$ of machine time and $24\, \text{hours}$ of craftsman's time. What number of rackets and bats must be made if the factory is to work at full capacity?

The maximum value of $Z=10 x+25 y$ subject to $0 \leq x \leq 3, 0 \leq y \leq 3, x+y \leq 5, x \geq 0, y \geq 0$ is

The shaded part of the given figure indicates the feasible region. Then the constraints are