In this session let me help you go through basically on Problems on Linear Programming problems. With the following examples you will come to know how to solve LPP.
Problem 1
Solve the following linear programming problem graphically:
Maximize Z = 4x + y ... (1)
subject to the constraints:
x + y ≤ 50 ....(2)
3x + y ≤ 90 ... (3)
x ≥ 0, y ≥ 0 ... (4)
Solution -
The shaded region in the below figure helps to understand graphical feasible region determined by the system of constraints (2) to (4). We observe that the feasible region OABC is bounded. So,
we now use Corner Point Method to determine the maximum value of Z.
The coordinates of the corner points O, A, B and C are (0, 0), (30, 0), (20, 30) and
(0, 50) respectively. Now we evaluate Z at each corner point. This will also help us in factoring calculator.
--> Problem 1
Solve the following linear programming problem graphically:
Maximize Z = 4x + y ... (1)
subject to the constraints:
x + y ≤ 50 ....(2)
3x + y ≤ 90 ... (3)
x ≥ 0, y ≥ 0 ... (4)
Solution -
The shaded region in the below figure helps to understand graphical feasible region determined by the system of constraints (2) to (4). We observe that the feasible region OABC is bounded. So,
we now use Corner Point Method to determine the maximum value of Z.
The coordinates of the corner points O, A, B and C are (0, 0), (30, 0), (20, 30) and
(0, 50) respectively. Now we evaluate Z at each corner point. This will also help us in factoring calculator.
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