假定企业的生产函数为q=10L^1/2K^1/2，单位劳动成本为20美元，单位资本成本为80美元。

(1)企业目前的产量为100单位，成本最小化的劳动和资本分别为20和5。在图上用等产量线和等成本线表示出来。

(2)企业想将产量扩大为140单位，如果资本在短期固定，需要多少劳动？在图形上表示出来，并计算企业新的成本。

(3)在图形上表示出企业在长期生产140单位产品的成本最小化劳动和资本投入。

(4)如果边际技术替代率为K/L,计算生产140单位产品的最优劳动和资本投入。

Suppose that a firm' s production is q= 10L1/2K1/2. The cost of a unit of labor is $ 20 and the cost of a unit of capital is $ 80. a The firm is currently production 100 unis of output and has determined that the cost - mini-mizing quantities of labor and capital are 20 and 5, respectively. Graphically illustrate this using isoquants and isocost lines.

b，The firm now wants to increase output to 140 units. If capital is fixed in the short run, how much labor will the firm require？ Illustrator this graphically and find the firms new total cost.

c. Graphically identify the cost - minimizing level of capital and labor in the long run if the firm wants to produce 140 units.

d. If the marginal rate of technical substitution is K/L, find the optimal level of capital and labor required to produce the 140 units of output.