Answer:
The maximum is at (0,4)
Step-by-step 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)
