The shaded area in the figure below is the solution set for a certain linear programming problem. The linear constraints are given by:

$A$ company makes $3$ models of calculators: $A, B$ and $C$ at factory $I$ and factory $II.$ The company has orders for at least $6400$ calculators of model $A, 4000$ calculators of model $B$ and $4800$ calculators of model $C.$ At factory $I, 50$ calculators of model $A, 50$ of model $B$ and $30$ of model $C$ are made every day; at factory $II, 40$ calculators of model $A, 20$ of model $B$ and $40$ of model $C$ are made every day. It costs $Rs. 12000$ and $Rs. 15000$ each day to operate factory $I$ and $II,$ respectively. Find the number of days each factory should operate to minimize the operating costs and still meet the demand.

The minimum value of $Z = 5x + 8y$ subject to the constraints $x + y \geq 5$,$0 \leq x \leq 4$,$y \geq 2$ 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 $.....$

The shaded region in the following figure represents the solution set for a certain linear programming problem. The linear constraints for this region are given by: