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 and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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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