A local garage uses two types of inputs, capital and labour, to service used cars. Their production function is described by Q = 8K^0.8L^0.2, where Q is the number of cars serviced, K is the amount of capital, equipment and tools used in the process and L denotes the input of human labour. The costs of inputs are £16 per unit of labour and £1 per unit of capital. The garage has received an order from a taxi company to service a fleet of 48 cars. Consider a constrained cost minimisation problem and answer the following questions.
a. What is the cost minimising quantity of capital the garage should use?
K* =
b. What is the cost minimising quantity of labour the garage should use?
L* =
c. What is the lowest cost at which 48 cars can be serviced?