Equation with two variables
- Thread starter george43
- Start date
Equation
This is what I have:
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*K+10*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=
This is what I have:
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*K+10*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=
Ah, now we are getting somewhere.
First, your equations are slightly incorrect. The question uses words like "cannot exceed" and "at most", so your equations will need to be rewritten to show this.
Since we have two equations, we can get creative.
Try to arrange one of the equations so that you have one variable alone on one side. You now have a way to express one variable in terms of the second.
Then, you can substitute this into the other equation. This new equation will have only a single variable, and you can solve for it.
Last, use the answer you've just found to solve for the other variable.
------------------------------------------------
Example
A+B = 5
2A + B = 7
First, rearrange to get A alone....
A = 5-B
Now, substitute this into the second equation.
2A + B = 7
2(5-B) + B = 7
10-2B + B = 7
10-B = 7
-B = -3
B=3
Now, we can solve for A.
A+B=5
A + 3 = 5
A = 2
First, your equations are slightly incorrect. The question uses words like "cannot exceed" and "at most", so your equations will need to be rewritten to show this.
Since we have two equations, we can get creative.
Try to arrange one of the equations so that you have one variable alone on one side. You now have a way to express one variable in terms of the second.
Then, you can substitute this into the other equation. This new equation will have only a single variable, and you can solve for it.
Last, use the answer you've just found to solve for the other variable.
------------------------------------------------
Example
A+B = 5
2A + B = 7
First, rearrange to get A alone....
A = 5-B
Now, substitute this into the second equation.
2A + B = 7
2(5-B) + B = 7
10-2B + B = 7
10-B = 7
-B = -3
B=3
Now, we can solve for A.
A+B=5
A + 3 = 5
A = 2
D
Deleted member 4993
Guest
Please correct your work as suggested and re-post
The equations are like that in the book. I don't understand why they are multiplying 8 *K.