A farmer owns 100 hectares of land to grow crops A, B, and C. The costs to grow crops A, B, and C per hectare are $ 40, $ 60, and $ 80, respectively. The farmer has 12,000 dollars in planting costs. The energy needed to cultivate plants A, B, and C per hectare is 10 hours of work, 15 hours of work, and 20 hours of work, respectively. The farmer has 4,000 hours available. The farmer wants to use all the land, all the budget for planting costs, as well as all available labor. a. Model a system of linear equations for the problem using a matrix representation! b. Solve the system of linear equations by eliminating Gauss or Gauss-Jordan to determine the area of land to plant each crop.!
A farmer owns 100 hectares of land to grow crops A, B, and C. The costs to grow crops A, B, and C per hectare are $ 40, $ 60, and $ 80, respectively. The farmer has 12,000 dollars in planting costs. The energy needed to cultivate plants A, B, and C per hectare is 10 hours of work, 15 hours of work, and 20 hours of work, respectively. The farmer has 4,000 hours available. The farmer wants to use all the land, all the budget for planting costs, as well as all available labor. a. Model a system of linear equations for the problem using a matrix representation! b. Solve the system of linear equations by eliminating Gauss or Gauss-Jordan to determine the area of land to plant each crop.!
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 21E
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A farmer owns 100 hectares of land to grow crops A, B, and C. The costs to grow crops A, B, and C per hectare are $ 40, $ 60, and $ 80, respectively. The farmer has 12,000 dollars in planting costs. The energy needed to cultivate plants A, B, and C per hectare is 10 hours of work, 15 hours of work, and 20 hours of work, respectively. The farmer has 4,000 hours available. The farmer wants to use all the land, all the budget for planting costs, as well as all available labor.
a. Model a system of linear equations for the problem using a matrix representation!
b. Solve the system of linear equations by eliminating Gauss or Gauss-Jordan to determine the area of land to plant each crop.!
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