Afirm 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=

a.

Input limit:

Budget limit:

b.

L=20

K=80

Explanation:

Ok, you save me a little bit of work and resolved the point a.

Indeed, the equations for Input limit and Budget limit are the ones you put in the question.

Now I will show you how to find the quantities of the two inputs in order to have a maximum output taking into account the input limit and the budget limit:

First, we need to put our equations in function of one of the variables, lets do it with L (Labor):

Input limit:

Budget Limit:

Now we match the 2 equations and find the value of K

L=L

Now that we have the optimum K we replace in any of the two equations to find the optimum L

And then we replace in the Input limit and Budget limit equations to verify:

Input limit:

Budget Limit:

answer: a. the kind of population living in your neighbourhood.

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