MHTCET 19 Apr 2026 Shift 2 Paper

Concept:A linear programming problem (LPP) is formed by identifying the objective function that needs to be optimized and all the given constraints on the decision variables.Explanation:Profit on each executive class ticket is Rs $1500$.Profit on each economy class ticket is Rs $900$.So total profit is $z = 1500x_1 + 900x_2$.Since the airline wants to maximize profit, the objective is Maximize $z$.The maximum passenger capacity gives:$x_1 + x_2 \leq 250$.At least 30 seats are reserved for executive class:$x_1 \geq 30$.At least 4 times as many passengers prefer economy class over executive class:$x_2 \geq 4x_1$.The number of passengers cannot be negative, so:$x_1 \geq 0$, $x_2 \geq 0$.Thus, the required LPP is:$$\text{Maximize } z = 1500x_1 + 900x_2$$subject to:$$x_1 + x_2 \leq 250, \quad x_1 \geq 30, \quad x_2 \geq 4x_1, \quad x_1, x_2 \geq 0.$$Answer:The correct option is D.