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Yes I understand what do to. But I have serious problems with seperating the cost function.
But there is no necessity of deriving those?

\[C(x,y)=\begin{cases} 100+qx^{0.5}+qy^{0.5}+qx+qy\,, & qx>0,qy>0\\ 0\,, & qx=qy=0 \end{cases}\] Which one is the right function? This one is the right one. With ^0.5. I had first problems with visualizing the formulae. So it should be first derived, right? 0.5 qx^0.5 + 0.5 qy^0.5 = ? But t...

To be the function \[C(x,y)=\begin{cases} 100+1.5\,qx+1.5\,qy\,, & qx>0,qy>0\\ 0\,, & qx=qy=0 \end{cases}\] subadditive it should be: \begin{align*} C\big((qx_1,qy_1)+(qx_2,qy_2)\big)\leqslant C(qx_1,qy_1)+C(qx_2,qy_2) \end{align*} for all $(qx_1,qy_1),(qx_2,qy_2)\in X\times Y$. But to proc...

Suppose the joint production of goods $X$ and $Y$ is described by the following cost function: $C(qx,qy) = 0$ if $qx,qy = 0$ and $100 + qx0.5 + qy0.5 + (qx + qy)$ if $qx,qy > 0$ Over what values of $qx$ and $qy$, if any, will $C(qx,qy)$ be subadditive? Can somebody help me how I can solve this quest...