what are the quantities of 2 inputs the firm must buy in order to produce a maximum output, given input and budget constraints?
input limit K+ L = 100
budget limit 8L + 10K =840
Firm buys 2 inputs, labor L and capital K, the total amt cannot exceed 100. The wage is $8 and the rental rate is $10. The firm can at most spend $840 on the two inputs.
Assume the output is maximized when the labour L is maximized (more people working = more output) and the capital is maximized (more investment = better results) and that labour and capital are equally important as regards output.
We have that 1) amt `L + K <= 100`
And 2) budget limit `8L + 10K <= 840`
Substituting `K = 100-L` into 2) we have
`8L + 10(100-L) <=840`
`implies` `2L >= 160` `implies` `L>=80`
This implies that `K<=20`
If labour and capital investment are equally important to output then the company should hire `L=80` labour and invest `K=20` monies.