I am asked to solve the following problem:
The problem:
You were asked to repair a farm house with sheets of plywood.
You were given thirty sheets of plywood. (each size = 10ft x 10ft)
The house requires 20 circles (radius = 2.5ft ) and 15 rectangles (size = 6ft x 4ft)
It costs 20 dollars to cut a circle and 15 dollars to cut a rectange. And there are three ways to cut the sheets as shown below:
(I set these into x,y,z: numbers of sheets cut in the way)
You can also buy 1 single circle with 45 dollars and 1 rectangle with 30 dollars.
You CANNOT waste more than 30% of the material. (Assuming total unused area <= 30%)
Here is how I solve the problem:
$x,y,z$ - numbers of sheets cut in the ways shown above
Objective function:
$M = 80x + 60y + 55z \tag{1}$
Constraints:
$$4x + 2z \le 20 \tag{2}$$ $$4y + z \le 15 \tag{3}$$ $$x + y + z \le 30 \tag{4}$$ $$0.215x + 0.04y + 0.367z \le 0.3(x+y+z) \tag{5}$$
It seems that I am getting all zero but I cannot figure out how to set the constraints.
I am asked to solve this with ortools
in Python.
But it doesn't make any sense to do it with the incorrect equations.