MHT CET202526 Apr 2025Evening ShiftMathematicsLinear ProgrammingActual
A manufacturing company produces two items, A and B. Each toy should be processed by two machines, I and II. Machine I can be operated for maximum 10 hours 40 minutes. It takes 20 minutes for an item A and 15 minutes for B. Machine II can be operated for a total time at 8 hours 20 minutes. It takes 5 minutes for an item A and 8 minutes for B . The profit per item of A is ₹ 25 and per item of B is ₹18. The formulation
Options
- Aaligned & Maximize z =25 x+18 y & subject to 20 x+15 y 640 & array r 5 x+8 y 500 x, y 0 array aligned
- Barray r Maximize z =25 x+18 y subject to 20 x+15 y 640 5 x+8 y 500 x, y 0 array
- Caligned & Maximize z =25 x+18 y & subject to 20 x+5 y 8 & 5 x+8 y 10 & x, y 0 aligned
- Darray r Maximize z =25 x+18 y subject to 4 x+3 y 128 array r 5 x+8 y 500 x, y 0 array array
Correct answer
B. array r Maximize z =25 x+18 y subject to 20 x+15 y 640 5 x+8 y 500 x, y 0 array
Step-by-step solution
The linear programming problem requires maximizing profit given machine time constraints. Let x and y represent the quantities produced of items A and B respectively. The objective function to maximize is Z = 25x + 18y , representing the total profit. Machine I operates for 640 minutes (10 hours 40 minutes), with processing times of 20 minutes per unit of A and 15 minutes per unit of B, yielding the constraint 20x + 15y 640 . Machine II operates for 500 minutes (8 hours 20 minutes), with processing times of 5 minut