1. A firm's production function isf(x₁,x₂)= y=(min{x₁, 5x₂})^1/2. If the price of factor 1 isw₁=$5 per unit and the price of factor 2 isw₂=$25 per unit, derive the total cost function (function of y) and the supply function (function of output price, p).
2. A competitive firm has a long-run total cost functionc(y)=3y²+675 fory>0 andc(0)=0. Derive the long-run supply function.