The point at which the maximum value of $Z = 3x + 2y$ subject to the constraints $x + 2y \leq 2$,$x \geq 0$,$y \geq 0$ occurs is $.....$

The feasible region (shaded) for a $LPP$ is shown in the adjacent figure. Maximize $Z = 5x + 7y$.

For a linear programming problem,the objective function is $Z = 3x + 9y$. The corner points of the feasible region are $(0, 10), (5, 5), (15, 15),$ and $(0, 20)$. The maximum value of $Z$ is . . . . . . .

An aeroplane can carry a maximum of $200$ passengers. $A$ profit of $Rs. 1000$ is made on each executive class ticket and a profit of $Rs. 600$ is made on each economy class ticket. The airline reserves at least $20$ seats for executive class. However,at least $4$ times as many passengers prefer to travel by economy class than by the executive class. Determine how many tickets of each type must be sold in order to maximize the profit for the airline. What is the maximum profit?

For a linear programming problem,the objective function is $Z = 8000x + 12000y$. If the corner points of the feasible region are $(0,0)$,$(20,0)$,$(12,6)$,and $(0,10)$,then the maximum value of $Z$ occurs at which corner point?

$z = 30x - 30y + 1800$ is an objective function. The corner points of the feasible region are $(15, 0), (15, 15), (10, 20), (0, 20),$ and $(0, 15)$. $z$ has the minimum value at $\ldots$ point.