For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. i.e: Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) Problem: Two machines, A and B produce items at the rate of 50 units per hour and 40 units per hour respectively. Under certain production plan, the total number of items needed is at least 1,000 items, the total number of hours available for running the machines is at most 24 hours. If the hourly cost is ₽300 for machine A and ₽250 for machine B, how many hours should each machine be used in order to minimize the cost?
For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables.
i.e:
Max Z = 500x + 300y
Subject to:
4x + 2y <= 60 (1st constraint)
2x + 4y <= 48 (2nd constraint)
x, y >= 0 (non-negativity)
Problem: Two machines, A and B produce items at the rate of 50 units per hour and 40 units per hour respectively. Under certain production plan, the total number of items needed is at least 1,000 items, the total number of hours available for running the machines is at most 24 hours. If the hourly cost is ₽300 for machine A and ₽250 for machine B, how many hours should each machine be used in order to minimize the cost?
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