business mathematics

Bida federal centre has three (3) departments, which services the main
operating departments of the hospital. The three are maintenance,
laundry and catering. In each case part of he services produced is
within the departments. Past records show the proportions of such
services to be as follows: maintenance 5% to itself, 25% and 105 to
laundry and catering respectively. Laundry 5% to maintenance and 10%
to catering 55 to itself, 10% and 15% to maintenance and laundry
respectively in a given period direct costs allocated to the operating
of each of these departments are shown is:
maintenance N56,000
Laundry N150,000
Catering N56,000
You are required to
a(i) Draw up the cost equation to derive the gross operating cost of
each of the service departments.
(ii) Demonstrate, both algebraically and numerically, the matrix
algebra steps which would lead to obtaining the inverse matrix to
solve the unknown value in the equation of the (i) above.
b You are given the following as the inverse matrix for the problem of (a) above.
1.083 0.067 0.125
0.293 1.034 0.194
0.145 0.116 1.086

You are required; using the matrix to obtain the gross cost of
operation of each service department working must be shown.

(HINT DO NOT ATTEMPT TO INVERT THE MATRIX)