
Matrix
A certain medical foundation receives money from two
sources: donations and interest earned on endowments. Of
the donations received, 30% is used to defray the costs of
raising funds; only 10% of the interest is used to defray the
cost of managing the endowment funds. Of the rest of the
money (the net income), 40% is used for research and 60%
is used to maintain medical clinics. Of the three expenses
(research, clinics, and fundraising), the portions going to
materials and personnel are divided according to Table
2.3. Find a matrix M such that if p is the value of dona
tions and q is the value of interest, then
M
[p]
[q ]
=
[m]
[f]
where m and f are the material and personnel costs of the
foundation, respectively.
Research Clinics Fundraising
material costs 80% 50% 70%
personnel costs 20% 50% 30%