The feasible region of an $LPP$ is shown in the figure. If $z=11x+7y$,then the maximum value of $z$ occurs at

The function to be maximized is given by $Z=2x+y$. The feasible region for this function $Z$ is the shaded region shown in the figure. The maximum value of $Z$ is . . . . . . and occurs at the point . . . . . . .

For the following shaded region,the linear constraints are:

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:

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.

$A$ company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type $A$ require $5 \text{ minutes}$ each for cutting and $10 \text{ minutes}$ each for assembling. Souvenirs of type $B$ require $8 \text{ minutes}$ each for cutting and $8 \text{ minutes}$ each for assembling. There are $3 \text{ hours } 20 \text{ minutes}$ available for cutting and $4 \text{ hours}$ for assembling. The profit is $Rs. 5$ each for type $A$ and $Rs. 6$ each for type $B$ souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?