Question

Solve the following linear program using the graphical solution procedure: Max 5A + 5B s.t. 1A lessthanorequalto 100 1B lessthanorequalto 80 2A + 4B lessthanorequalto 400 A, B greaterthanorequalto 0

Answer 1

Answer:

• The optimal solution to the given linear programming problem exist at (100,50)

• and the optimal solution is:  5A+5B= 750

Step-by-step explanation:

We are given  a system of linear programming problem as follows:

   Max 5A + 5B

s.t.        A ≤ 100---------------(1)

            B ≤ 80-------------(2)

          2A+4B ≤400-------------(3)

which is given by:

            A+2B ≤ 200

and   A,B≥0

This means that the solution to this LPP  will lie in the first quadrant.

( Since, both the variables A and B are greater than or equal to zero)

Now, we consider that A is represented by the  x axis and B by y-axis.

We know that the optimal solution always exist at the boundary point.

Hence, by plotting these inequalities in the graph we get the boundary points as:

(0,0) , (0,80) , (100,0) , (100,50) and (40,80)

Now, we will check at which boundary point the optimal function is maximized .

   Point        Value of optimal function( 5A+5B)

    (0,0)                           0

   (0,80)                         400

   (100,0)                        500

  (100,50)                       750

   (40,80)                        600

The maximum value is obtained at (100,50).

and the value of the optimal solution is:  750