# Maths Help

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A local garage uses two types of inputs, capital and labour, to service used cars. Their production function is described by Q = 10K0.7L0.3, 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 £20 per unit of labour and £2 per unit of capital. The garage has received an order from a taxi company to service a fleet of 32 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 32 cars can be serviced?

TC* =
0
X

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