Solve the ofllowing maximization problem graphically maxz 3

Solve the ofllowing maximization problem graphically: maxz = 3x_1 + 2x_2 2x_1 + x_2 less than or equal to 100 x_1 + x_1 less than or equal to 80 x_1 less than or equal to 40 x_1 greater than or equal to 0 x_2 greater than or equal to 0

Solution

Answer :-

So far we have learnt how to construct a mathematical model for a linear programming problem. If we can find the values of the decision variables x₁, x₂, x₃, ..... x_n, which can optimize (maximize or minimize) the objective function Z, then we say that these values of x_i are the optimal solution of the Linear Program (LP).

The graphical method is applicable to solve the LPP involving two decision variables x₁, and x₂, we usually take these decision variables as x, y instead of x₁, x₂. To solve an LP, the graphical method includes two major steps.

a) The determination of the solution space that defines the feasible solution. Note that the set of values of the variable x₁, x₂, x₃,....x_n which satisfy all the constraints and also the non-negative conditions is called the feasible solution of the LP.

b) The determination of the optimal solution from the feasible region.

a) To determine the feasible solution of an LP, we have the following steps.

So far we have learnt how to construct a mathematical model for a linear programming problem. If we can find the values of the decision variables x1, x2, x3, ..... xn, which can optimize (maximize or minimize) the objective function Z, then we say that these values of xi are the optimal solution of the Linear Program (LP).

The graphical method is applicable to solve the LPP involving two decision variables x1, and x2, we usually take these decision variables as x, y instead of x1, x2. To solve an LP, the graphical method includes two major steps.

a) The determination of the solution space that defines the feasible solution. Note that the set of values of the variable x1, x2, x3,....xn which satisfy all the constraints and also the non-negative conditions is called the feasible solution of the LP.

b) The determination of the optimal solution from the feasible region.

a) To determine the feasible solution of an LP, we have the following steps.