# Solve equations using the $\max$ function

How do you address formulas that entail the $\max$ function? As an example:. $$\max(8-x, 0) + \max(272-x, 0) + \max(-100-x, 0) = 180$$

In this instance, I can exercise in my head that $x = 92.$ But what is the basic procedure to make use of when the variety of $\max$ terms are approximate? Many thanks for the aid, below is a Python remedy for the trouble if any person is interested.

```
def solve_max(y, a):
y = sorted(y)
for idx, y1 in enumerate(y):
y_left = y[idx:]
y_sum = sum(y_left)
x = (y_sum - a) / len(y_left)
if x <= y1:
return x
print solve_max([8, 272, -100], 180)
```

3

Björn Lindqvist 2022-07-25 20:42:42

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