The maximum value of $Z=3x+5y$,subject to the constraints $x+4y \leq 24$,$y \leq 4$,$x \geq 0$,$y \geq 0$ 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. If the profit on a racket and on a bat is $Rs. 20$ and $Rs. 10$ respectively,find the maximum profit of the factory when it works at full capacity.

The difference between the maximum value and minimum value of the objective function $z = 3x + 5y$ of a linear programming problem subject to constraints $5x + 10y \leq 50$, $x + y \geq 1$, $y \leq 4$, $x \geq 0$, $y \geq 0$ is $3\lambda$. Then the value of $\lambda$ is

An airplane can carry a maximum of $250$ passengers. $A$ profit of $\text{Rs } 1500$ is made on each executive class ticket and a profit of $\text{Rs } 900$ is made on each economy class ticket. The airline reserves at least $30$ seats for executive class. Also, at least $4$ times as many passengers prefer to travel by economy class than by executive class. Let $x_1$ be the number of passengers in executive class and $x_2$ be the number of passengers in economy class. Formulate the Linear Programming Problem $(LPP)$ to maximize the profit for the airline.

Solution of the following $LP$ problem
Minimize $z = -3x + 2y$
subject to $0 \leq x \leq 4, 1 \leq y \leq 6, x + y \leq 5$ is $.....$

Minimize the objective function $Z = 3x + 2y$ subject to the constraints: $x + y \geq 8$,$x + y \leq 5$,$x \geq 0$,$y \geq 0$.