Question

The daily cost of operating a hospital is a linear function of the number of in-patients I, and out-patients, P plus a fixed cost a i.e
C = a + bP + dI
Given the following data from 3 days, find the value of a, b and d by setting up a linear system of equations and using the inverse matrix

Answer 1

Answer:

Step-by-step explanation:

c=a+bp+dl

6950 = a + 10b +40d -------------(1)

6725 = a + 9b + 35d -------------(2)

7100 = a + 12b + 40d -------------(3)

From (1) and (3)

250=2b

b=125.

Answer 2

Given :   The daily cost of operating a hospital is a linear function of the number of in-patients I, and out-patients, P plus a fixed cost a i.e

C = a + bP + dI

To find : value of a, b and d

Solution:

C   = a   +  bP  + dl

a + 10b  + 40d  = 6950      Eq1

a + 9b  + 35d   = 6725     Eq2

a  + 12b  + 40d  =  7100    Eq3

Eq3 - Eq1

=> 2b = 150

=>  b = 75

Eq1 - Eq2

=> b + 5d  =  225

=> 75 + 5d = 225

=> 5d  = 150

=> d  = 30

putting in Eq1

=> a + 750 + 1200 = 6950

=> a  =  5000

a = 5000   b  = 75    d  = 30

Lets verify

a + 10b  + 40d  = 5000 + 750  + 1200  = 6950      

a + 9b  + 35d   = 5000 + 675 +  1050 =  6725      

a  + 12b  + 40d  = 5000 + 900 + 1200 =  7100    

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