0

I'm having trouble setting up this problem. A firm produces 4 kinds of goods: G1, G2,G3,G4. Each good requires three kinds of input: Labor, Row Materials, Capital (quantity if each input needed for each good is noted in the table below) There are 14 units of Labor, 15 units of row materials, and 10 units of capital. Find quantity of each good if all inputs are utilized in these goods production. G1 uses 3 L, 2 RM, 1 C g2 uses 2 L, 5 RM, 2 C g3 uses 2 L , 2 RM, 2 C g4 uses 1 L, 3 RM, 3 C

I know that each good is a sum of inputs and the question is asking how many of each good can I produce using all the inputs. Any help or suggestion on setting up this problem will be appreciated

Harry Peter
  • 7,819
John
  • 15
  • If you sell $g_1$ amount of good type $1$, how much labor is used in the process? $3g_1$, right? If you sell $g_2$ amount of good type $2$, how much labor is used for this? Continuing, how much labor is used total from the perspective of how much of each good we used? What does the problem statement tell us about how much labor we use? This gives us a first equation, $3g_1+2g_2+2g_3+1g_4=14$. Do so similarly for the remaining two kinds of input. Solve the corresponding system via gaussian elimination. Finally, make sure any answer (or answers) make sense (non-negative, integer,...) – JMoravitz Aug 01 '16 at 07:02
  • I began setting up the equation up that way and I wanted to see if I was on the right track. Thank you for answering my question – John Aug 01 '16 at 07:14

0 Answers0