# what are the quantities of 2 inputs the firm must buy in order to produce a maximum output, given input and budget constraints? L= K= Data: input limit K+ L = 100 budget limit 8L + 10K =840...

what are the quantities of 2 inputs the firm must buy in order to produce a maximum output, given input and budget constraints?

L=

K=

Data:

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.

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### 1 Answer

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.**