Final answer:
The optimal combination of factors of production is where a firm's isoquant touches the isocost line, indicating maximal output at minimal costs and achieving equilibrium. This does not relate to achieving full employment or obtaining government subsidies but rather to efficient resource utilization.
Step-by-step explanation:
The optimal combination of factors of production refers to the mix of labor, capital, and other resources that maximize production output while minimizing production costs. In economic terms, this point is where the isoquant curve, representing all the different combinations of factors that produce a certain level of output, touches the isocost line, which represents all the different combinations of factors that can be purchased with a certain budget. At this point of tangency, the firm is said to be in equilibrium as it cannot produce more output without increasing costs or it cannot lower costs without reducing output.
Productive efficiency is achieved when production is on the production possibilities frontier, and in a perfectly competitive market, firms will operate where the market price is equal to the minimum of the long-run average cost curve. Allocative efficiency is realized when the chosen point on the production possibility frontier reflects the socially preferred output mix.
This is where the firm can no longer produce one good without sacrificing the production of another. The optimal combination is necessarily the one that does neither lead to unemployment nor relies on government subsidies; it's solely focused on the efficiency of resource use.