Given the system of constraints, name all vertices of the feasible region. then find the maximum value of the given objective function. constraints: x is greater than or equal to 0 y is greater than or equal to 0 y is less than or equal to 1/3x+3 5 is greater than or equal to y+x objective function: c=6x-4y

The constraints are given by:

( Since, in the first quadrant both the x and y values are positive )

Ques 1)

The feasible region that is formed with the help of these inequality is:

                     Quadrilateral ABCD.

Also, the vertices of the feasible region are:

A(0,3)

B(1.5,3.5)

C(5,0)

D(0,0)

Ques 2)

We know that the objective function is checked at the boundary points of the feasible region i.e. vertices of the feasible region.

The objective function is:

C=6x-4y

              C=6×0-4×3

                 i.e.

               C= -12

            C=6×1.5-4×3.5

                  i.e.

                C= -5

           The value of objective function is:

                 C=6×5-4×0

                        i.e.

                      C=30

                      C=6×0-4×0

                          i.e.

                        C=0

The maximum value of the objective function is: 30

and it is obtained at the vertex C(5,0)

answer: huh

step-by-step explanation: