A firm has a production functionf(x₁,x₂)=x₁^1/3x₂^2/3. The price ofx₁=1 and the price ofx₂=2. Denote the output by y. Derivethe conditional demand forx₁(equation for the y and cost minimizingx₁)andcost function c(y). If the market price is given by 2,what is the profit maximizing output? If the firm has limit of output which is 100, then derivethe supply curve of this firm(note that in this case of deriving the supply curve, you should consider the general price, not 2).