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
  Maximize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \leq 250, x_1 \leq 30, x_2 \leq 4x_1, x_1 \geq 0, x_2 \geq 0$.
• B
  Minimize $z = 150x_1 + 90x_2$ subject to $x_1 + x_2 \leq 250, x_1 \geq 30, x_2 \geq 4x_1, x_1 \geq 0, x_2 \geq 0$.
• C
  Minimize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \leq 250, x_1 \geq 30, x_2 \geq 4x_1, x_1 \geq 0, x_2 \geq 0$.
• D
  Maximize $z = 1500x_1 + 900x_2$ subject to $x_1 + x_2 \leq 250, x_1 \geq 30, x_2 \geq 4x_1, x_1 \geq 0, x_2 \geq 0$.