To determine To calculate: The daily cost Private Room (regular care), Private Room (Maximum Care), semiprivate room (regular care), and semiprivate room (Maximum care). Explanation Given: Total daily costs in January: $ 24 , 040 Total daily costs in April: $ 23 , 926 Total daily costs in July: $ 23 , 760 Total daily costs in October: $ 24 , 042 The table shows the number of patients in each category: REGULAR CARE PATIENTS: Month Semiprivate Private January 22 8 April 26 8 July 24 14 October 20 10 MAXIMUM CARE PATIENTS: Month Semiprivate Private January 60 10 April 54 12 July 56 6 October 62 8 Explanation: Calculation: Let, daily cost for a private room (regular care) is a , daily cost for a private room (maximum care) is b , daily cost for the semiprivate room (regular care) is c , and daily cost for the semiprivate room (maximum care) is d . 22 c + 8 a + 60 b + 10 d = 24040 26 c + 8 a + 54 c + 12 d = 23926 24 c + 14 a + 56 c + 6 d = 23760 20 c + 10 a + 62 c + 8 d = 24042 The coefficient matrix is: A= [ 22 8 60 10 26 8 54 12 24 14 56 6 20 10 62 8 ] Consider the provided data, the matrix equation is: [ 22 8 60 10 26 8 54 12 24 14 56 6 20 10 62 8 ] [ c a d b ] = [ 24040 23926 23760 24042 ] AX=B X=A − 1 B Calculate A − 1 by use of Gauss Jordan elimination. The augmented matrix is: [ 22 8 60 10 1 0 0 0 26 8 54 12 0 1 0 0 24 14 56 6 0 0 1 0 20 10 62 8 0 0 0 1 ] Apply R 1 → R 1 22 , [ 1 0.36 2.72 0.45 0.045 0 0 0 26 8 54 12 0 1 0 0 24 14 56 6 0 0 1 0 20 10 62 8 0 0 0 1 ] Apply, R 2 → R 2 − 26 R 1 , R 3 → R 3 − 24 R 1 , R 4 → R 4 − 20 R 1 [ 1 0.36 2.72 0.45 0.045 0 0 0 0 − 1.36 − 16.72 0.3 − 1.17 1 0 0 0 5.36 − 9.28 − 4.8 − 1.08 0 1 0 0 2.8 7.6 − 1 − 0.9 0 0 1 ] Apply R 2 → − R 2 1.36 , [ 1 0.36 2.72 0.45 0.045 0 0 0 0 1 12.29 − 0.22 0.86 0.73 0 0 0 5.36 − 9.28 − 4.8 − 1.08 0 1 0 0 2.8 7.6 − 1 − 0.9 0 0 1 ] Apply R 1 → R 1 − 0.36 R 2 , R 3 → R 3 − 5.36 R 2 , R 4 → R 4 − 2

12th Edition

ISBN: 9780134776323

Author: MULLINS

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Chapter 6.6, Problem 22E

To determine

To calculate: The daily cost Private Room (regular care), Private Room (Maximum Care), semiprivate room (regular care), and semiprivate room (Maximum care).

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Chapter 6.6, Problem 21E

Chapter 6.6, Problem 23E

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