Answered: The Johnson Farm has 500 acres of land…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.2: Systems Of Three Linear Equations In Three Variables

Problem 30PS

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Question

The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $42 and $32 per acre, respectively. Jacob Johnson has $18,600 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant?

Formulate a system of equations that can be used to find the solution where x is the number of acres of corn planted and y is the number of acres of wheat planted. (Do not perform any row operations.)

	=	500
	=	18,600

Write the augmented matrix corresponding to the system. (Do not reorder the equations. Let the first column represent x and the second column represent y.)

500

18,600

Using the Gauss-Jordan elimination method, pivot the matrix about the first entry in the first row. State the result.