# Perfect complement outputs with each output being composed of substitutable inputs

How does one solve the following maximization problem?

$\underset{K_1, K_2, L_1, L_2}{\text{maximize }} min\{K_1 + L_1,K_2 + L_2\}$

subject to $c(K_1 + \mu K_2) + \beta c(L_1 + \mu L_2)$

where $c(.)$ is a cost function that is increasing and convex in its argument, and $\mu$ and $\beta$ are exogenous parameters.

• What does Maximize min mean? – BKay Oct 27 '16 at 0:05
• @BKay, we're maximizing for a firm that has two outputs but can only sell the minimum of both outputs. Each output is produced with capital and labor that are perfectly substitutable. This is like maximizing a leontief utility (or min utility). – damamaharaj Oct 27 '16 at 0:15