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%