The isoquant curve shows all the inputs that produces the same level of output. The isocost line shows a combination of all the factors of production that have the same cost. A firm is always looking to minimize costs so that they can produce maximum output with minimum input with a given quality.

The point of minimization is where a given level of ouput is produced with the minimum costs possible because it increases efficiency. Cost is minimized at the point where the slope of the isoquant curve (marginal rate of technical substitution) is equal to the slope of the isocost line (wage/rent in case of two inputs i.e labor and capital) i.e the point of tangency as shown in the figure as E. The amount of labor and capital hired at the minimum point are L0 and K0 respectively.