Answer:
a.
Input limit: [tex]K+L=100[/tex]
Budget limit: [tex]8K+10L=840[/tex]
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:
[tex]K+L=100[/tex]
[tex]L=100-K[/tex]
Budget Limit:
[tex]8K+10L=840[/tex]
[tex]L=\frac{840-8K}{10}[/tex]
[tex]L=84-0.8K[/tex]
Now we match the 2 equations and find the value of K
L=L
[tex]100-K=84-0.8K[/tex]
[tex]100-84=-0.8K + K[/tex]
[tex]0.2K=16[/tex]
[tex]K=\frac{16}{0.2}[/tex]
[tex]K=80[/tex]
Now that we have the optimum K we replace in any of the two equations to find the optimum L
[tex]L=100-80=20[/tex]
And then we replace in the Input limit and Budget limit equations to verify:
Input limit:
[tex]80 + 20 = 100[/tex]
Budget Limit:
[tex]8(80)+10(20)=840[/tex]
Answer:
L= 80
K= 20
Explanation:
The guy who solved this question he perfectly explained but he did mistake on putting a correct answer at L=20 and K=80. Just reverse the L and K mistake.
