Find the maximum value of 2x+3y subject to the constraints

Question

Find the maximum value of 2x+3y and the point at which it occurs subject to the following constraints:

y>(or = to) 3x-9

y<(or=to) x+5

y<(or=to)-2x+11

x>(or=to) 0, y>(or=to) 0

Answer 1

Step 1:

The objective function is .

The constraints are

.

Graph :

Graph the inequalities and shade the required region.

Note : The shaded region is the set of feasible solution for the objective function including boundary segments.

Observe the graph:

Tabulate the solutions of each of two system of inequalities and obtain the intersection points.

Step 2:

Find the value of objective function at the intersection points.

The objective function is .

At point : .

At point : .

At point : .

At point : .

At point : .

Observe the values of :

The maximum value of is when and .

Solution:

The maximum value of the objective function is at the point .