multiple choice. choose the one alternative that...
TRANSCRIPT
Midterm - Finite
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use graphical methods to solve the linear programming problem.
1) Minimize z = 4x + 5y
subject to: 2x - 4y ≤ 10
2x + y ≥ 15
x ≥ 0
y ≥ 0
1) _______
A) Minimum of 20 when x = 5 and y = 0 B) Minimum of 75 when x = 0 and y = 15
C) Minimum of 39 when x = 1 and y = 7 D) Minimum of 33 when x = 7 and y = 1
2) Maximize z = 8x + 12y
subject to: 40x + 80y ≤ 560
6x + 8y ≤ 72
x ≥ 0
y ≥ 0
2) _______
A) Maximum of 120 when x = 3 and y = 8 B) Maximum of 100 when x = 8 and y = 3
C) Maximum of 92 when x = 4 and y = 5 D) Maximum of 96 when x = 9 and y = 2
A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a given
week. Use the table to find the system of inequalities that describes the manufacturer's weekly production.
3) Use x for the number of chairs and y for the number of tables made per week. The number of
work-hours available for construction and finishing is fixed.
3) __
__
__
_
A) 3x + 4y ≤ 48
3x + 3y ≤ 42
x ≥ 0
y ≥ 0
B) 3x + 3y ≤ 48
4x + 3y ≤ 42
x ≥ 0
y ≥ 0
C) 3x + 4y ≤ 48
3x + 3y ≤ 42
x ≤ 0
y ≤ 0
D) 4x + 3y ≤ 48
3x + 3y ≤ 42
x ≥ 0
y ≥ 0
4) Use x for the number of chairs and y for the number of tables made per week. The number of
work-hours available for construction and finishing is fixed.
4) _______
A) x + y ≥ 36
3x + 2y ≥ 0
27x + 20y ≥ 0
B) x + 3y ≥ 27
x + 2y ≥ 20
C) x + 3y ≥ 0
x + 2y ≥ 0
x ≤ 27
y ≤ 20
D) x + 3y ≤ 27
x + 2y ≤ 20
x ≥ 0
y ≥ 0
Use the Gauss-Jordan method to solve the system of equations.
5) 5x - y + z = 8
7x + y + z = 6
12x + 2z = 14
5) _______
A)
B)
C)
D)
6) 4x + 2y - z = 7
x - 8y - 9z = -94
6x + y + z = 29
6) _______
A) ( -3, 2, 6) B) No solution C) ( 3, 2, 9) D) ( 3, 9, 2)
Graph the linear inequality.
7) x + y < -3
D)
Perform the indicated operation.
10)
Let A = and B = . Find 2A + B.
10) ______
A)
B)
C)
D)
Find the inverse, if it exists, of the given matrix.
11)
11) ______
A)
B)
C)
D)
12)
A =
12) ______
A)
B)
C)
D)
State the linear programming problem in mathematical terms, identifying the objective function and the constraints.
13) A breed of cattle needs at least 10 protein and 8 fat units per day. Feed type I provides 6 protein
and 2 fat units at $ 4/bag. Feed type II provides 2 protein and 5 fat units at $ 2/bag. Which
mixture fills the needs at minimum cost?
13) ______
A) Minimize 4x + 2y
Subject to: 6x + 2y ≥ 10
2x + 5y ≥ 8
x,
y
≥
0.
B) Minimize 4x + 2y
Subject to: 6x + 2y ≥ 8
2x + 5y ≥ 10
x, y ≥ 0.
C) Minimize 2x + 4y
Subject to: 6x + 2y ≥ 10
2x + 5y ≥ 8
x, y ≥ 0.
D) Minimize 4x + 2y
Subject to: 6x + 2y ≤ 8
2x + 5y ≤ 10
x, y ≤ 0.
14) A car repair shop blends oil from two suppliers.
Supplier I can supply at most 41 gal with 3.6% detergent. Supplier II can supply at most 67
gal with 3.2% detergent. How much can be ordered from each to get at most 100 gal of oil with
maximum detergent?
14) ______
A) Maximize 0.032x + 0.036y
Subject to: x ≤ 41
y ≤ 67
x + y ≤ 100.
B) Maximize 0.036x + 0.032y
Subject to: 0 ≤ x ≤ 41
0 ≤ y ≤ 67
x + y ≤ 100.
C) Maximize 41x + 67y
Subject to: x ≥ 41
y ≥ 67
0.036x + 0.032y ≥ 100.
D) Maximize 41x + 67y
Subject to: x ≤ 41
y ≤ 67
0.036x + 0.032y ≤ 100.
Solve the problem by writing and solving a suitable system of equations.
15) Alan invests a total of $ 10,500 in three different ways. He invests one part in a mutual fund
which in the first year has a return of 11%. He invests the second part in a government bond at
7% per year. The third part he puts in the bank at 5% per year. He invests twice as much in the
mutual fund as in the bank. The first year Alan's investments bring a total return of $ 825. How
much did he invest in each way?
15) ______
A) mutual fund: $ 2400; bond: $ 6900: bank: $ 1200
B) mutual fund: $ 3600; bond: $ 5100: bank: $ 1800
C) mutual fund: $ 3000; bond: $ 7000: bank: $ 1500
D) mutual fund: $ 3000; bond: $ 6000: bank: $ 1500
Find the value(s) of the function, subject to the system of inequalities.
16) Find the maximum and minimum of subject to:
0 ≤ x ≤ 10, 0 ≤ y ≤ 5, 3x + 2y ≥ 6.
16) ______
A) 130, 90 B) 90, 24 C) 40, 24 D) 130,18
Graph the feasible region for the system of inequalities.
17) 2y + x ≥ -2
y + 3x ≤ 9
y ≤ 0
x ≥ 0
D)
Solve the inequality.
20) The equation can be used to determine the approximate profit, y in dollars, of
producing x items. How many items must be produced so the profit will be at least
20) ______
A) 0 < x ≤ 1,121,299 B) x < 1,121,300
C) x ≥ 1,120,700 D) x ≥ 1,121,300
21) Fantastic Flags, Inc., finds that the cost to make x flags is while the revenue
produced from them is (C and R are in dollars). What is the smallest whole number of
flags, x, that must be sold for the company to show a profit?
21) ______
A) 210 B) 1,147,222 C) 124,024 D) 1938
Solve the system of equations. If the system is dependent, express solutions in terms of the parameter z.
22) x + y + z = -1
x - y + 2z = -8
2x + y + z = 2
22) ______
A) ( 3, 1, -5) B) No solution C) ( -5, 3, 1) D) ( -5, 1, 3)
Given the matrices A and B, find the matrix product AB.
23)
A = , B = Find AB.
23) ______
A) AB is not defined. B)
C)
D)
Decide whether the pair of lines is parallel, perpendicular, or neither.
24) 3x - 8y = -14
32x + 12y = -15
24) ______
A) Perpendicular B) Parallel C) Neither
Solve the system of two equations in two variables.
25) 4x + 6y = 2
20x + 30y = 10
25) ______
A)
B)
for any real number y
C) D) No solution
Solve the matrix equation for X.
26)
A = , B = , AX = B
26) ______
A)
B)
C)
D)
Solve the problem.
27) What is the size of the matrix?
27) ______
A) 3 B) 3 x 2 C) 6 D) 2 x 3
28) The height h in feet of a projectile thrown upward from the roof of a building after time t
seconds is shown in the graph below. How high will the projectile be after 3.3 s?
28) ______
A) 500 ft B) 450 ft C) 550 ft D) 600 ft
29) The diagram shows the roads connecting four cities.
W X
Y Z
Ho
w
ma
ny
wa
ys
are
ther
e to
trav
el
bet
wee
n cities
W and
Z by
passing
throug
h at
most
one
city?
(Hint:
Write a
matrix,
A, to
represent
the
number
of routes
between
each pair
of cities
without
passing
through
another
city.
Then
calculate
).
29) ___
___
A) 4 B) 5 C) 1 D) 3
30) If A is a 3 × 3 matrix and A + B = is the zero matrix, what can you say about the matrix? 30) ______
A) B is the 3 × 3 identity matrix B) B = -A
C) B is the 3 × 3 zero matrix D) B = A
Determine whether the given ordered pair is a solution of the given equation.
31) + = 9; ( 1, -2) 31) ______
A) Yes B) No
Find the x-intercepts and y-intercepts of the graph of the equation.
32) -4x + 2y = 4 32) ______
A) x-intercept: -1; y-intercept: 2 B) x-intercept: -4; y-intercept: -2
C) x-intercept: -2; y-intercept: -4 D) x-intercept: 2; y-intercept: -1
Perform the indicated operation where possible.
33)
-
33) ______
A)
B)
C)
D)
Find the slope and the y-intercept of the line.
34) 6y + 7x = -7 34) ______
A) m = -7; b = -7 B)
m = - ; b = -
C) m = 6; b = 0 D)
m = ; b = 0
35) 6x - 5y = -5 35) ______
A) m = 0; b = 6 B) m = -6; b =
-1
C)
m = ; b =
-5
D)
m = ; b = 1
Graph the linear equation.
36) 12y = 2x - 14
36) ______
A)
B)
C)
D)
Find the production matrix for the input-output and demand matrices.
37)
A = D =
37) ______
A)
B)
C)
D)
Find the value(s) of the function on the given feasible region.
38) Find the maximum and minimum of
38) ______
A) -96.25, -138 B) -138, 0 C) 75, -138 D) 75, 0
39) Find the maximum and minimum of
39) ______
A) 45, 27 B) 215, 27 C) 170, 27 D) 215, 170
Provide an appropriate response.
40) If a system of inequalities includes then the feasibility region is restricted to what? 40) ______
A) The region right of and including x = 1 B) The region left of and including x = -1
C) The region right of and including x =
-1
D) The region left of and including x = 1
1) D
2) B
3) A
4) D
5) B
6) C
7) A
8) A
9) A
10) B
11) C
12) B
13) A
14) B
15) D
16) D
17) A
18) B
19) A
20) D
21) D
22) A
23) A
24) A
25) B
26) D