given the system of constraints name all vertices the find maximum value
x>_ 0
y>_ 0
y<_1/5x+1
4>_ y+x
To find the maximum value of the system of constraints, we need to determine the vertices of the feasible region and evaluate the objective function at each vertex.
First, let's draw the graph of the inequalities to visualize the feasible region:
1. Start by plotting the lines corresponding to the equations y = 1/5x + 1 and y = -x + 4. These are the lines where the inequalities for y < or = to 1/5x + 1 and 4 > or = y + x are satisfied.
2. Since x > or = 0 and y > or = 0, draw the coordinate axes (x-axis and y-axis) starting from the origin (0,0).
Now, let's find the vertices of the feasible region:
1. Choose any two intersecting lines from the graph.
2. Find the intersection point of the two lines. Let's name this point A. This intersection point represents a vertex of the feasible region. Mark the coordinates of point A.
3. Repeat steps 1 and 2 for different combinations of lines until you find all the vertices of the feasible region.
Once you have identified all the vertices, substitute the coordinates of each vertex into the objective function and calculate the value. The maximum value will correspond to the vertex that yields the highest objective function value.
Note: The objective function is not provided in your question, so make sure to specify the objective function to determine the maximum value.