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

Attached the solution and work.

Answer with explanation:

The constraints are given by:

               

The first and second constraints tells that the solution must lie in the first quadrant including the origin )

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

Also, the third inequality is a solid line ( since the inequality is not strict i.e. it is a inequality with a equality sign ) that passes through (-9,0) and (0,3) and the shaded region is towards the origin ( since the inequality passes the zero point test ).The fourth inequality is a solid line ( since the inequality is strict ) that passes through (5,0) and (0,5) and the shaded region is towards the origin ( since the inequality passes the zero point test)

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

We check at A(0,3)

              C=6×0-4×3

                 i.e.

               C= -12

at B(1.5,3.5)

            C=6×1.5-4×3.5

                  i.e.

                C= -5

at C(5,0)

           The value of objective function is:

                 C=6×5-4×0

                        i.e.

                      C=30

and at D(0,0)

                      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)

Istg idk..if there all the same length there all the same number but use google

Think of it as five or above give it a shove. change the 5 or above to the right to a zero and add one to the number on the left.