1. Consider a firm with the following production function f(z1,z2,z3)=z1+min{z2,z3}. The market prices for all goods arle positive, i.e. p>0,w1>0,w2>0, and w3>0. ) Derive the profit function and show that Hotelling lemma holds. ) State the cost minimization problem (CMP). ) Write down the Lagrangian function of CMP and derive the optimality conditions (FOCs). [Hint: the answer to part (c) still applies here] 1. Consider a firm with the following production function f(z1,z2,z3)=z1+min{z2,z3}. The market prices for all goods arle positive, i.e. p>0,w1>0,w2>0, and w3>0. ) Derive the profit function and show that Hotelling lemma holds. ) State the cost minimization problem (CMP). ) Write down the Lagrangian function of CMP and derive the optimality conditions (FOCs). [Hint: the answer to part (c) still applies here]