The maximum value of $z = 9x + 13y$ subject to the constraints $2x + 3y \leq 18$,$2x + y \leq 10$,$x \geq 0$,$y \geq 0$ is:

The correct constraints for the given feasible region are:

Reshma wishes to mix two types of food $P$ and $Q$ in such a way that the vitamin contents of the mixture contain at least $8$ $units$ of vitamin $A$ and $11$ $units$ of vitamin $B$. Food $P$ costs Rs $60/kg$ and Food $Q$ costs Rs $80/kg$. Food $P$ contains $3$ $units/kg$ of Vitamin $A$ and $5$ $units/kg$ of Vitamin $B$ while food $Q$ contains $4$ $units/kg$ of Vitamin $A$ and $2$ $units/kg$ of vitamin $B$. Determine the minimum cost of the mixture. Let the mixture contain $x$ kg of food $P$ and $y$ kg of food $Q$. Therefore,$x \geq 0$ and $y \geq 0$. The given information can be compiled in a table as follows:

The solution of the linear programming problem,maximize $Z = 3x_{1} + 5x_{2}$ subject to $3x_{1} + 2x_{2} \leq 18$,$x_{1} \leq 4$,$x_{2} \leq 6$,$x_{1} \geq 0$,$x_{2} \geq 0$ is:

The maximum value of $z=6x+8y$ subject to the constraints $x-y \geq 0$,$x+3y \leq 12$,$x \geq 0$,$y \geq 0$ 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.