I have an optimization problem where I'd like to maximize revenue and I have separate variables for cost and revenue.
- Building a single unit of a product takes 100 hours of labor
- I have a list of staff, the number of hours they have available, and the cost per hour for each
- The projected revenue of the product changes based on the total cost to build the unit
- If cost is less than 2500, revenue = 40 * cost
- If cost is between 2500 to 5000, revenue = 25 * cost
- If cost is > 5000, revenue = 8 * cost
- I want my objective function to maximize the appropriate revenue formula based on what the cost might be
I tried to use the BigM notation to determine which range the cost falls into, and then my objective function looked something like
is_cost_group_1 * (40 * cost) +
is_cost_group_2 * (25 * cost) +
is_cost_group_3 * (8 * cost))
but this gave me an error'ed saying the solver does not support quadratic functions.
Is this possible as a linear programming problem?