Optimization of the company's cash flow

Figure n°1: Determination of optimal capital compromise between solvency and profitability.
The C function passes through a minimum when its derivative with respect to the Working Capital Fund is zero. This
method of calculation is thus similar to the previous. The same criticism can be formulated in its regard.
(c) Optimize the use of the Working Capital Fund.
This approach is original to the extent that it reverses the terms of problem (1). The selected objective is maximization
of benefit based on a constraint, the Fund available bearing or 'cash '. In these circumstances, for example if the
production function is represented by:
C = 20 + 5 (x)
(Total cost = fixed costs + unit variable costs multiply by the quantity produced), and the available capital funds and
150 maximum production will be:
150 = 20 + 5(x)
x = 26 units
If it is assumed that the unit selling price is 10, and that the revenue (or turnover) function has the form:
R = 10 (x)
The maximum benefit allowed by the available working capital fund will be:
P = R - C = 10 x - (20 + 5 x) or P = 110 (1)
The marginal benefit will represent the maximum price that can pay the company for additional funds required for
the production of one unit more.
As can be seen, the interest of this model lies in its didactical value. It has the merit to describe the relationships
between the operational needs and the Working Capital Fund. But it seems devoid of practical interest because the
simplifying assumptions on which it is based, as well as elsewhere, because the methodology adopted. We can take
the same approach in the context of 'mathematically' more complex situations:
When functions are not linear (the cost equation becomes
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