Download 9x − 5y = 4 −5x + 3y = 7 3 −1 2 16 5 2 −6 18 2 −3 2 7 3x − y + 2z = 16

FINITE MATHEMATICS TEST ONE SAMPLE QUESTIONS.
SHOW ALL CALCULATIONS AND SIMPLIFY ANSWERS. ACTUAL TEST PROBLEMS MAY DIFFER FROM THESE.
Page 1 of 2.
(6 points)
1. Multiply the matrices.
(5 points)
2. The matrix
9 −5
−5 3
3 2
4 3
5 −3
3 −3
−5 7
has inverse
=
3/2 5/2
.
5/2 9/2
Use this fact and
matrix multiplication to solve the system
9x − 5y = 4
−5x + 3y = 7
B −1
(12 points)
3. Find
by the Gauss-Jordan procedure, if B =
(12 points)
4. Given the input-output matrix
0.25 0.25
0.40 0.20
4 −2 3
5 −3 3
7 −2 7
and the demand matrix
60
40
the production matrix.
(12 points)
(3 points)
5. Find the reduced row echelon matrix for
6. Solve the system
Go to page 2.
3 −1 2 16
5 2 −6 18 .
2 −3 2 7
3x − y + 2z = 16
5x + 2y − 6z = 18
2x − 3y + 2z = 7
Hint: See Problem 5.
find
FINITE MATHEMATICS TEST ONE SAMPLE QUESTIONS.
SHOW ALL CALCULATIONS AND SIMPLIFY ANSWERS. ACTUAL TEST PROBLEMS MAY DIFFER FROM THESE.
Page 2 of 2.
(20 points)
 x m 0, y
 x + 4y [
7. (a) Graph the system of inequalities. 
x + y [

 3x + y [
m 0,
24,
9,
21





Make a large graph, shade the feasible set in your graph, and
give coordinates of its vertices.
(4 points)
(4 points)
(b) Find the values of x and y to maximize
the conditions in part (a).
P = 7x + 3y subject to
(c) On the graph for part (a), draw a broken line for P = 43.
8. We need to make sure our pet dinosaur gets 1000 mg of vitamin A,
2500 units of vitamin C, and 500 units of vitamin D, every day.
One bag of food X provides 100 units of of vitamin A, 200 units of vitamin C and
100 units of vitamin D, and costs $1.50. One bag of food Y provides 90 units of
vitamin A, 210 units of vitamin C and 120 units of vitamin D per day and costs
$1.80. We have to buy enough of each type of food to meet the dinosaur’s
nutritional requirements, and we want to do it at the least cost.
(10 points)
(a) Set up all appropriate inequalities for x bags of food X,
and y bags of food Y, daily.
(2 points)
(b) Write a formula for the cost.
(10 points)
9. (a)Find the slope-intercept equation of the line of best fit for the four points
(2, 1 ), (3, 4), (4, 6), (6, 7 )
(b) Find the linear corrrelation, r
( 100
points3.total. )
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