Question

Maximize
P=60x+50y .

x+y≤80
5x+10y≤560
50x+20y≤1600
x≥0
y≥0

Just need help in finding s=

Answer 1

I wish I knew more about what method you are using, graphical, analytical, or computer. I will explain grahical.

Draw the lines on an x y graph (x horizontal) , scale x from zero to 150, y from zero to 80

Line 1: x=0
line 2: y=0
line 3: y=-x+80
line 4: y=-2.5x+80
line 5: y=-0.5x+56
those are from the constraints given.

Now look: an area is enclosed. Within that area is the "area of acceptable solutions to the constraints". Now we have a very nice theorem that tells us somewhere on the boundary (usually at the corner intersections) will be the maximum or minimum of any profit function. Your function is P=60x+50y
figure that value for each corner. Obviously, the minimum will be at (0,0). Find the coordinates (x,y) for the maximum.