(In here I stuck in Lagrange formula, don't what to do for the step).
1) It is known that a new company has cobb-douglas production functions i.e. : f(K; L)= 50L2/5 K3/5. Labor wages are $100, and capital rent is $200. The ability of the owner of the company to finance the purchase of inputs is $30,000. Question: what is the maximum output that the new company can generate? Write down the formulation of the approach: minimization or maksimization.
2) Suppose known a folding table company has a production function are: f(K;L) = L1/2K1/2. The input price for the capital is $3 and the wage is $9. The company wants to produce at least 100 folding tables. What is the amount of manpower and capital needed to realize the company's shortness? What is the total costs that must be borne by the company? Write down the formulation of the approach: minimization or maksimization.
3) A kitchen appliance company with the trademark "Meza" has a cost structure
Long-term average is: LRAC(Q) = 40-6Q+Q2/3. The market demand for kitchen equipment brand "Meza" is D(P) = 2200 + 100P. The question is: (a) the long-term quantity balance of each company; (b) price balance; and (c) the number of companies on the market.
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