"Los Sureos" is a company producing orange jam. Its production function can be represented as follows: q=f(T,L,K)=4T1/2L1/4K1/4

where the production of jars of orange jam (q) depends on land (T), labor (L), and capital (K). Assume that land is measured in hectares, labor in number of workers, and capital in number of machines. "Los Sureos" owns a large field of 10,000 hectares that is used entirely for the production of orange. The fixed cost of maintenance (for the entire 10,000 hectares) is $2.000. On the other hand, the number of workers and machinery to be used are not fixed. The average wage per worker is $1,600, and the rental cost per machine is $100.

(a) State the problem of the firm that minimizes costs in the short run.

(b) Find the conditional demand functions for labor and capital.

(c) Indicate how many workers and machinery the company would hire, if it wishes to produce 8,000 jars of orange jams.

(d) Find the total cost function (C (q)) relating output and total cost (TC), and the average cost (AC) and marginal cost (MC) functions.

(e) Indicate what type of returns to scale "Los Sureos" has. Show your calculations. Explain.