How to write cost slabs in objective function of Linear Programming?

Let say I have a variable Income per month, over a period of 1 to 12 months my total Income is 1700 $, I want to minimize tax on this income.
How should I write this objective function in abstract algebra form
Z = 1000 * 0.05 + 500 * 0.10 + 200 * 0.15

basically I want to put slab wise tax on total income, any suggestion ?

I have three slabs 0-1000, 1000-1500, >1500
tax per slab 0.05, 0.10, 0.15

1 Answer
1

Here is an example implementation in python:

def tax(x):
if (x <= 1000):
return x * 0.05
elif (x <= 1500):
return 50 + (x - 1000) * 0.1
else:
return 100 + (x - 1500) * 0.15

income = 100
while (income < 5000):
print ("Taxes on income of " + str(income) + ": " + str(tax(income)))
income += 250


You could parameterize the steps and rates if you wanted.

If you need to regress a piecewise function from results, you can use numpy.piecewise.

numpy.piecewise

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