MHT CET202619 April 2026Evening ShiftMathematicsLinear ProgrammingActual
An airplane can carry a maximum of 250 passengers. A profit of Rs 1500 is made on each executive class ticket and a profit of Rs 900 is made on each economy class ticket. The airline reserves at least 30 seats for executive class. However at least 4 times as many passengers prefer to travel by economy class than by executive class. Let x₁ be the number of passengers of executive class and x₂ be the number of passenge
Options
- AMaximize z = 1500x₁ + 900x₂ subject to x₁ + x₂ 250 , x₁ 30 , x₂ 4x₁ , x₁ 0, x₂ 0 .
- BMinimize z = 150x₁ + 90x₂ subject to x₁ + x₂ 250 , x₁ 30 , x₂ 4x₁ , x₁ 0, x₂ 0 .
- CMinimize z = 1500x₁ + 900x₂ subject to x₁ + x₂ 250 , x₁ 30 , x₂ 4x₁ , x₁ 0, x₂ 0 .
- DMaximize z = 1500x₁ + 900x₂ subject to x₁ + x₂ 250 , x₁ 30 , x₂ 4x₁ , x₁ 0, x₂ 0 .
Correct answer
D. Maximize z = 1500x₁ + 900x₂ subject to x₁ + x₂ 250 , x₁ 30 , x₂ 4x₁ , x₁ 0, x₂ 0 .
Step-by-step solution
Let x₁ be the number of executive class passengers and x₂ be the number of economy class passengers. The profit on each executive class ticket is Rs 1500 and on each economy class ticket is Rs 900 . The objective is to maximize the total profit z , which is given by: Maximize z = 1500x₁ + 900x₂ The airplane can carry a maximum of 250 passengers, which gives the constraint: x₁ + x₂ 250 The airline reserves at least 30 seats for executive class, which gives: x₁ 30 At least 4 times as many passengers prefer to travel