A firm buys two inputs, labor L and capital K, the total amount of which cannot exceed 100. The wage is $8, and the rental rate is $10. The firm can at most spend $840 on the two inputs.

a. Write the two equations:

Input limit: K + L = 100

Budget limit: 8 x K + 10 x L = 840

b. What are the quantities of two inputs the firm must buy in order to produce a maximum output, given input and budget constraints?

L=

K=