Trig/Math Anal
HW NO.
LP-1
LP-2
LP-3
LP-4
LP-4
LP-5
LP-5
Name_______________________No_____
SECTIONS
Cramer’s
Rule
3-Variable
Systems
ASSIGNMENT
DUE
√
Pg. 125/wr 7, 9, 11
Pg. 710-11/1, 3, 5
Pg. 419/13, 17 Pg. 420/1, 9
Practice Set A
Practice Set B
Practice Set C
Practice Set D
Practice Set E
Practice Set F
Writing Assignment: Write a linear programming
problem. Include a topic sentence (i.e., “A factory
produces tables and chairs…”), supporting details (the
facts), and a conclusion (the question). State your
problem and solve it.
Next Test Date:
Practice Set A: Graphing
Graph
1. x  0, y  0, x  2 y  8, 3x  2 y  12
2. 0  x  10, 0  y  20, 2 x  y  32
Practice Set B: Linear Programming
1. The snack bar cooks and sells burgers and hot dogs at football games. To stay in business it
must sell at least 10 burgers but can’t cook more than 40. It must also sell at least 30 hot dogs
but can’t cook more than 70. The snack bar cannot cook more than 90 burgers and hot dogs in
all. The profit on a burger is 33¢ and the profit on a hot dog is 21¢. How many of each sandwich
should it sell to make a maximum profit? What is the maximum profit possible?
2. A manufacturer can show a profit on a bicycle of $6 and a profit on a tricycle of $4.
Department A requires 3 hours to manufacture the parts for a bicycle and 4 hours to
manufacture parts for a tricycle. Department B takes 5 hours to assemble a bicycle and 2 hours
to assemble a tricycle. How many bicycles and tricycles should be produced to maximize the
profit if the total time available in department A is 450 hours and in department B is 400 hours?
4. Find a system of inequalities for the graph:
5 2 1 4
(2, 7)
1 0 3 5
3. Use minors to evaluate
(-4, 3)
4 0 1 6
7 3 2 1
(8, -3)
875090532 Page 1
Practice Set C: Linear Programming
1. Graph and find the corner points: 0  x  9, 0  y  10,  2 y  3x  29, x  y  12
2. You are about to take a test that contains question types A worth 10 points each and question
type B worth 25 points each. You must do at least 3 questions of type A but time restricts doing
more than 12. You must do at least 4 questions of type B but time restricts doing more than 15.
In total you can do no more than 20 questions. How many of each type of question must you do
to maximize your score? What is this maximum score?
3. An airline with two types of airplanes, P-1 and P-2, has contracted with a tour group to provide
accommodations for a minimum of each of 2000 first class, 1500 tourist and 2400 economy-class
passengers. Airplane P-1 costs $12,000 per mile to operate and can accommodate 40 first-class,
40-tourist and 120 economy-class passengers, whereas airplane P-2 costs $10,000 per mile to
operate and can accommodate 80 first-class, 30 tourist, and 40 economy-class passengers. How
many of each type of airplane should be used to minimize the operating cost? What is the
minimum cost?
0 0 2 0 0
3 1 5 0 4
4. Use minors to evaluate 1 2 6 0 2
1 3 10 2 5
4 2 15 1 6
Practice Set D: Linear Programming
1. Suppose there are two kinds of synthetic foods, K rations and C rations. These foods contain
the following nutritional components:
Food
K rations
C rations
Calories per
ounce
100
200
Protein per ounce
Fat per ounce
50
10
0
30
Suppose the minimum daily requirements for an active person are 2500 calories, 350 units of
protein and 150 units of fat. Which food or combination of foods should be used in order to fulfill
the minimum daily requirements and minimize total weight?
2. A truck gardener has a plot of 50 acres and decides to plant two different vegetables, B and C.
He has a maximum of 185 man-hours of labor and $205 to spend for seed. B requires 4 manhours per acres for cultivation and C requires 1 man-hour per acre. Seed for B costs $2 per acre
and for C, $5 per acre. If B sells for $27 per acre profit and C for $14 per acre profit, how many
acres of each should be planted to maximize profit?
2 1 0 1 3
1 2 0 1 0
3. Use minors to evaluate 1 2 0 3 0
15 12 4 7 50
1 5 0 1 2
Practice Set E: Linear Programming
1. A parking lot has a total of 600 sq meters of space. A car needs 6 sq meters, a bus 30 sq
meters of space. The lot attendant must park at least 30 cars, but can handle a maximum of 60
vehicles. A car costs $5 to park, a bus $8. How many of each should be parked to maximize
revenue? Find the revenue.
875090532 Page 2
2. Graph x  6, y  3, x  3y  9, 3x  y  6 ; minimize 3x  4 y
3. Two different colors of paint are to be mixed. Color A requires 1 unit of red, 4 of blue, per
gallon. Color B requires 6 units of red, 1 of blue, per gallon. There are at most, 54 units of red, 32
units or blue available. Find the maximum number of gallons of paint that can be mixed.
4. Two different crops are to be planted on, at most, 250 acres. There are at most 20 days
available to plant crops. Ten acres of corn can be planted in one day, 15 acres of soybeans in a
day. They cannot be planted at the same time. How many acres of each should be planted to
maximize profit if corn earns $30/acre and soybeans $25/acre?
2 x  5 y  4 z  1
2 1 0 5
5. Find x, y, and z if x  3 y  2 z  7
2 1 3 4
6. Use minors to evaluate
3x  y  z  5
0 5 2 6
1 4 1 0
Practice Set F: SAT Review
1. Find x
2. The figure shown is a square. Find its area.
3. The figure shown is an isosceles trapezoid.
Find x
4. The figure shown is an equilateral triangle.
Find x
5. Express y in terms of x
6. Find x and y
7. Find the product of the slopes of l , m, and n
8. Circle O has radius R; circle P has radius 3R.
area of circle O
Find the ratio: area of circle P
9. Isosceles triangle CAB is shown with
CA  BA, AB  6, BD  3. Find BAC
875090532 Page 3
10. Find the volume of the cylinder (V   r 2 h)
11. Find a 2  b 2
12. Find the area of ABC if radius = 7 and
AC  BC
13. Find the area of ABD if
AD  6, DC  3, and BC  4
14. Find x and y
15. The figure shown is a cube with AB  4 .
Find the perimeter of rectangle ADCB
16. The figure shown is a square enclosing a
semicircle with AD  4. Find the area of the
shaded region.
17. There are six right triangles
shown. Find x 2  y 2
ANSWERS
Practice Set B
1. 40 burgers, 50 hot dogs
18. Find x and y
2. 50 bicycles, 75 tricycles
19. Find  ,  and 
3. 13
5x  3 y  31
R
|
2 x  3 y  17
4. S
|T x  2 y  2
Practice Set C
1. (0,0) (9,0) (9,1) (5,7) (2,10) (0,10)
2. 5 A, 15 B, profit $425
3. 30 P-1, 10 P-2, min $460,000
4. 10
Practice Set D
1. 5 oz K rations, 10 oz C rations
2. 45 acres B, 5 acres C, profit $1285
3. 80
Practice Set E
1. 10 bus, 50 cars, $330
2. -0.3
3. 6 gal A , 8 gal B
172
75
4. 100 acres corn, 150 acres soybeans
6. 121
5. x  55 , y  55 , z  166
55
Practice Set F
1. 20
2. 26
3. 16
6. x  60, y  59
7. 1
11. 41
16. 16  2
12. 49
8. 19
13. 12
17. 21
18. x  32 , y  73
875090532 Page 4
4. 3
9. 60
5. y  2 x
10. 2 x 3
14. x  60, y  9 3
15. 8  8 2
19.   7.5,   45,  30