The total output of loudspeaker systems of the Acrosonic Company at their three production facilities for May and June is given by the matrices A and B, respectively. Model A Model B Model C Model D Location I 330 250 480 290 A = Location II 480 380 560 0 Location III 550 400 200 870 Model A Model B Model C Model D Location I 220 170 300 190 B = Location II 390 300 500 50 Location III 440 250 150 750 The unit production costs and selling prices for these loud speakers are given by matrices C and D, respectively. C = Model A 100 Model B 200 Model C 250 Model D 500 and D = Model A 160 Model B 250 Model C 360 Model D 710 Compute the following matrices, and explain the meaning of the entries in each matrix. (a) AC The entries of matrix AC give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June . (b) AD The entries of matrix AD give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June . (c) BC The entries of matrix BC give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.1: Matrix Operations

Problem 19EQ: A factory manufactures three products (doohickies, gizmos, and widgets) and ships them to two...

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The total output of loudspeaker systems of the Acrosonic Company at their three production facilities for May and June is given by the matrices A and B, respectively.

Model A

Model B

Model C

Model D

Location I

330

250

480

290

A =

Location II

480

380

560

Location III

550

400

200

870

Model A

Model B

Model C

Model D

Location I

220

170

300

190

B =

Location II

390

300

500

Location III

440

250

150

750

The unit production costs and selling prices for these loud speakers are given by matrices C and D, respectively.

C =

Model A

100

Model B

200

Model C

250

Model D

500

and D =

Model A

160

Model B

250

Model C

360

Model D

710

Compute the following matrices, and explain the meaning of the entries in each matrix.

(a) AC

The entries of matrix AC give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

(b) AD

The entries of matrix AD give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

The entries of matrix BC give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

(d) BD

The entries of matrix BD give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

(e)

(A + B)C

The entries of matrix (A + B)C give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

(f)

(A + B)D

The entries of matrix (A + B)D give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

(g)

A(D − C)

The entries of matrix A(D − C) give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

(h)

B(D − C)

The entries of matrix B(D − C) give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

(i)

(A + B)(D − C)

The entries of matrix (A + B)(D − C) give the total ---Select--- production costs revenue realized profits gained at locations I, II, and III for the month(s) of ---Select--- May June May and June .

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