Question

What point in the feasibility region maximizes the objective function?

Answer 1

In general, you solve a problem like this by identifying the vertices of the feasible region. Graphing is often a good way to do it, or you can solve the equations pairwise to identify the x- and y-values that are at the limits of the region.

In the attached graph, the solution spaces of the last two constraints are shown in red and blue, and their overlap is shown in purple. Hence the vertices of the feasible region are the vertices of the purple area: (0, 0), (0, 1), (1.5, 1.5), and (3, 0).

The signs of the variables in the contraint function (+ for x, - for y) tell you that to maximize C, you want to make y as small as possible, while making x as large as possible at the same time. The solution space vertex that does that is (3, 0).

Answer 2

Answer:

The point in the feasibility region which maximizes the objective function is:

                               (3,0)

Step-by-step explanation:

We know that the point which maximize or  minimize the objective functions are: the boundary points.

Hence, we plot these inequalities and find out the boundary points and check which point will maximize the objective function which is given by:

              C=  5x-4y

Based on the graph the boundary points are:

(0,0)  ,  (0,1)  , (1.5,1.5)  ,  (3,0)

At (0,0)

C= 5×0-4×0

C=0

At (0,1)

C=5×0-4×1

C= -4

At (1.5,1.5)

C=5×1.5-4×1.5

C=1.5

At (3,0)

C=5×3-4×0

C=15

Hence, we get that the point which maximize the objective function is:

                                    (3,0)