#### Summary

Two things determine profits: income, or turnover (the price at which we sell something) and costs (how much we spent making what we sell). Therefore, knowing how much our costs are going to be is essential when planning the viability of a business.Production maximisation must be seen as an optimisation problem regarding the *production function*, represented by *isoquants*, and a constraint regarding production costs, represented by an *isocost line*.

Producers are therefore faced with the following problem: faced with a set of possible production levels and a fixed budget, how to choose the level which maximises their production?

If we know the production function of a certain producer, and we know their budget, we have the two restrictions necessary to maximise their production. This can be done graphically, with the point where isocost and isoquant meet defining an optimum, as shown in the adjacent figure.

It can be also done mathematically, through a *Lagrangian*, where the first derivatives determine a system of equations that can be resolved by submitting our production function to the restriction presented by the budget:

**Video – Production maximisation:**