The Carver Foundation funds three nonprofit organizations engaged in alternative energy research activities. From past data, the proportion of funds spent by each organization in research on solar energy, energy from harnessing the wind, and energy from the motion of ocean tides is given in the accompanying table. org,IL org.2 or93 Proportion of Money Spent Wind Solar Tides Organization I Organization II Organization III 0.6 0.3 0.1 0.4 0.3 0.3 0.2 0.6 0.2 a) Formulate a system of equations to determine the total amount awarded to each organization if the total amount spent by all three organizations on solar, wind, and tidal research is $9.2 million, $9.6 million, and $5.2 million, respectively. b) Write the system of equations obtained in part (a) in matrix equation form. c) Solve the matrix equation from part (b).
The Carver Foundation funds three nonprofit organizations engaged in alternative energy research activities. From past data, the proportion of funds spent by each organization in research on solar energy, energy from harnessing the wind, and energy from the motion of ocean tides is given in the accompanying table. org,IL org.2 or93 Proportion of Money Spent Wind Solar Tides Organization I Organization II Organization III 0.6 0.3 0.1 0.4 0.3 0.3 0.2 0.6 0.2 a) Formulate a system of equations to determine the total amount awarded to each organization if the total amount spent by all three organizations on solar, wind, and tidal research is $9.2 million, $9.6 million, and $5.2 million, respectively. b) Write the system of equations obtained in part (a) in matrix equation form. c) Solve the matrix equation from part (b).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part C
Transcribed Image Text:) The Carver Foundation funds three nonprofit organizations engaged in alternative
energy research activities. From past data, the proportion of funds spent by each
organization in research on solar energy, energy from harnessing the wind, and
energy from the motion of ocean tides is given in the accompanying table.
Proportion of Money Spent
Wind
Solar
Tides
0.1
org,I emi
Organization I
Organization I
Organization III
0.6
0.3
2 10 m
org.?
or93 8mi
0.4
0.3
0.3
0.2
0.6
0.2
a) Formulate a system of equations to determine the total amount awarded to
each organization if the total amount spent by all three organizations on solar,
wind, and tidal research is $9.2 million, $9.6 million, and $5.2 million,
respectively.
b) Write the system of equations obtained in part (a) in matrix equation form.
c) Solve the matrix equation from part (b).
Expert Solution
Step 1
Consider the provided question,
(c)
Let x, y and z represents the three organizations (I, II and III) that spent amount on solar, wind and tidal energy respectively.
According to the given question, the system of equations is written as,
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