Explanation Given: Total number of hours for fabrication is 124, for painting is 68 and for packaging is 24. Procedure used: 1. Form an augmented matrix [ A | I ] where a matrix A is placed along with a same dimension identity matrix I separated by a line. 2. Apply row operations on [ A | I ] in order to obtain another augmented matrix [ I | B ] where I , is again an identity matrix and B is an inverse of A. 3. If the reduction process yields a row of zeros in the left half of the augmented matrix, then the inverse of A does not exist. Calculation: Let x , y and z be the number of 4-shelf metal, 6-shelf metal and 4-shelf wooden bookcases, respectively. The total number of hours for fabrication is 124, the first equation is 2 x + 3 y + 3 z = 124 . The total number of hours for painting is 68, the second equation is x + 1.5 y + 2 z = 68 . The total number of hours for packaging is 24, the third equation is 1 2 x + 1 2 y + 1 2 z = 24 . Thus, the system of equations becomes, { 2 x + 3 y + 3 z = 124 x + 1.5 y + 2 z = 68 1 2 x + 1 2 y + 1 2 z = 24 Convert the system of equation into a matrix notation. [ 2 3 3 1 1.5 2 1 2 1 2 1 2 ] [ x y z ] = [ 124 68 24 ] Take A = [ 2 3 3 1 1.5 2 1 2 1 2 1 2 ] and X = [ x y z ] and transform [ 2 3 3 1 1.5 2 1 2 1 2 1 2 ] [ x y z ] = [ 124 68 24 ] as follows. A − 1 A X = A − 1 [ 124 68 24 ] ( Multiply with A − 1 on RHS of both sides ) I X = A − 1 [ 124 68 24 ] ( ∵ A − 1 A = I ) X = A − 1 [ 124 68 24 ] Obtain the augmented matrix as follows. [ 2 3 3 1 0 0 1 1.5 2 0 1 0 1 2 1 2 1 2 0 0 1 ] Apply the row operation R 1 − 2 R 2 → R 2 and R 1 − 4 R 3 → R 3 and reduce the matrix. [ 2 3 3 1 0 0 0 0 − 1 1 − 2 0 0 1 1 1 0 − 4 ] Apply the row operation R 2 ↔ R 3 and reduce the matrix

5th Edition

ISBN: 9780134179926

Author: HARSHBARGER

Publisher: PEARSON CO

See similar textbooks

Videos

Question

Chapter 7.4, Problem 34E

To determine

To find: The number of each type of bookcases that can be produced.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.4, Problem 33E

Chapter 7.4, Problem 35E

Students have asked these similar questions

Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate of 0.35%. Use this information for all the problems below. 1. Find an exponential function f(t) that gives the population of Tattooine t years from now. (3 points)

A house was valued at $95,000 in the year 1988. The value appreciated to $170,000 by the year 2007. A) If the value is growing exponentially, what was the annual growth rate between 1988 and 2007? Round the growth rate to 4 decimal places. r = B) What is the correct answer to part A written in percentage form? r = 3 %.

B G R + K Match each equation with a graph above - 3(0.9)* 1 a. green (G) 3(1.5)* b. black (K) 3(0.73)* c. blue (B) d. red (R) I ✪ 4(1.21)* - 3(1.21)* e. orange (O)

Chapter 7 Solutions

EBK COLLEGE ALG.IN CONTEXT W/APPL.F/MAN

Ch. 7.1 - In Exercises 14, solve the systems of equations....Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The number of each type of bookcases that can be produced.

Solution Summary: The author calculates the total number of hours for fabrication, painting, and packaging.

Videos

To find: The number of each type of bookcases that can be produced.

Want to see the full answer?

Chapter 7 Solutions