A furniture produces three types of desks: a children’s mode…

A furniture produces three types of desks: a children’s model, an office model, and a deluxe model. Each desk is manufactured in three stages: cutting, construction, and finishing. The time requirements for each model and manufacturing stage are given below in the table. Each week the company has available a maximum of 100 hours for cutting, 100 hours for construction, and 65 hours for finishing. If all available time must be used, how many of each type of desk should be produced each week? a) Write the system of linear equations and augmented matrix. b) Show steps in using Gauss or Gauss-Jordan elimination to solve the system. (Answer without substantial work will receive a minimum score.) c) Write the answer in a complete sentence. 

Given the system of equations: a) Write the augmented matri…

Given the system of equations: a) Write the augmented matrix.   b) Use Gauss-Jordan elimination method to simplify the matrix to a reduced row-echelon form. Show your work! No steps shown – no credit given!   c) Write the solution set for the system of linear equations and check your answer.