Question

PLEASE HELP ME IF YOU CAN ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Identify the graph of the system of constraints then find the values of x and y that maximize the objective function.

Answer 1

The maximum is at (0,4)

Explanation:

x≥0

y≥0

x+y ≤4

2x+y ≤6

We need to plot the four inequalities. The left side has no axis. The max is at 4. The minimum is at 0 for the shaded area

When we have a system of constraints, the minimum and maximum are at the vertices of the graph

There are 4 points

(0,0)

The intersection point of the 2 lines which is (2,2)

The intersection at the y axis (0,4)

The intersection at the x axis is (3,0)

Once we have these points we put them into the constraint equation

C = 30x+50y

(0,0)

C = 0+0 = 0 This would be the trivial point since nothing happens

(0,4)

C = 0+50(4) = 200

(3,0)

C = 30*3 = 90

(2,2)

C = 30(2) + 50(2) = 60+100 = 160

The maximum is at (0,4)