Question 1109621: A farmer has 200 acres of land suitable for cultivating crops A, B and C. The cost per acre of cultivating crop A, crop B, and crop C is $40, $60 and $80, respectively. The farmer has $12,600 available for land cultivation. Each acre of crop A requires 20 labor-hours, each acre of crop B requires 25 labor-hours and each acre of crop C requires 40 labor-hours. The farmer has a maximum of 5950 labor-hours available. If he wishes to use all his cultivatable land, the entire budget and all the labor available, how many acres of each crop should he plant?
I would like to use the Gauss Jordan Elimination Method
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 200 acres of land available.
crop A cost per acre = 40
crop B cost per acre = 60
crop C cost per acre = 80
12,600 dollars available for land cultivation.
crop A requires 20 hours of labor for each acre.
crop B requires 25 hours of labor for each acre.
crop C requires 40 hours of labor for each acre.
maximum of 5950 hours of labor are available.
wants to use all the land, all the labor hours, all the money available.
wants to use gauss-jordan elimination method.
set up:
x = number of acres for crop A.
y = number of acres for crop B.
z = number of acres for crop C.
cost:
40 * x + 60 * y + 80 * z = 12,600.
labor hours:
20 * x + 25 * y + 40 * z = 5950
acres:
x + y + z = 200
set up your matrix and then feed into the gauss-jordan elimination calculator by greg thatcher for the easy way to find the answer.
greg thatcher gauss-jordan elimination calculator can be found here:
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
her's the output from my use of this calculator.
the procedure is shown in the following link:
http://pages.pacificcoast.net/~cazelais/251/gauss-jordan.pdf
i don't have time to do it for you today, but i can go through it tomorrow if you still need someone to show you step by step.
use the calculator to check your results.
use the method to figure out how to to it yourself.
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