CH 4
Name:
Form A
Period:
1. Find the graph of the equation 4x + 2y = 12.
c.
d.
2. Find the graph of the inequality 4x + 5y < 40.
b,
,0)
c.
(oxÿe)
d,
(0,4)
/ÿ'/.,j N,O)
3. Find the point of intersection of the lines whose equations are 4x + 2y = 12 and 3x + 9y
=39.
A) (5,-4)
rÿ) (10, 1)
\ C))(1, 4)
ÿFÿ
D) (2, 2)
,,
%.
Page 1
.
Graph the constraint inequalities for a linear programming problem shown below.
Which feasible region shown is correct?
4x+3y<24
x>O,y>_O
b,
lllliiiiilllÿ,ÿ,o)
)
(0,0)
°
Write a resource constraint for this situation: producing a plastic ruler (x) requires 10
grams of plastic while producing a pencil box (y) requires 30 grams of plastic. There
are 2000 grams of plastic available.
A) 200x + (2000/30)y <y- 2000
B) 30x+ 10y<2000
}ÿ)10x + 30y < 2000
D) x+y<2000
.
Write the resource constraints for this situation: Kim and Lyrm produce tables and
chairs. Each piece is assembled, sanded, and stained. A table requires 2 hours to
assemble, 3 hours to sand, and 3 hours to stain. A chair requires 4 hours to assemble, 2
hours to sand, and 3 hours to stain. The profit earned on each table is $20 and on each
chair is $12. Together Kim and Lyrm spend at most 16 hours assembling, 10 hours
sanding, and 13 hours staining.
2x+4y< 16, 3 x+2y< 10, 3x+ 3y < 13, x20,y>_O
B) 2x+3y+3z<20,4x+2y+ 3z<12, x>O,y>O,z>--O
C) 16x+10y+13z<0,2x+3y+3z<20,4x+2y+3z<-12'x>-0'y>0'z>-0
D) 8x + 4y < 16, (10/3) x + 5y < 10, (13/3)x + (13/3)y < 13, x >-- 0, y > 0
Page 2
7. Graph the feasible region identified by the inequalities:
4x+ ly< 12
2x+7y<28
x>O,y>O
b=
.,0)
(t4,0)
(3,0)
d,
\
--____
(0,3)"
_(ÿ2,0)
8. Given below is the sketch of the feasible region in a linear programming problem.
Which point is not in the feasible region?
-....
(0,4>
(0,0)
a) (0,4)
(4,0)
(6,0)
D) (1,2)
Page 3
9. Write a profit fornaula for this mixture problem: a small stereo manufacturer makes a
receiver and a CD player. Each receiver takes eight hours to assemble, one hour to test
and ship, and earns a profit of $30. Each CD player takes 15 hours to assemble, two
hours to test and ship, and earns a profit of $50. There are 160 hours available in the
assembly department and 22 hours available in the testing and shipping department.
A) P = 8x + ly
B) P = 160x + 22y
\ ,
= 15x + 2y
30X + 50y
10. The graph of the feasible region for a mixture problem is shown below. Find the point
that maximizes the profit function P = x + 4y.
(O,O)
,0)
(0,9)
s) (6, 7)
c) (7, 3)
D) (6, 0)
11. The feasible region for a linear programming mixture problem with two products is in
the first quadrant of the Cartesian plane.
• <:::::ÿ True
ÿ
B) False
12. An optimal solution for a linear programming problem will always occur at a corner
point of the feasible region.
True
B)----False
13. An optimal production policy for a linear programming mixture problem may eliminate
one product.
True
B) False
14. Suppose the feasible region has four corners at these points: (0, 0), (8, 0), (0, 12), and (4,
8). If the profit formula is $2x + $4y, what is the maximmn profit possible?
A) $16
BI $40
D) $54
/
"
.........
Page 4
15. Find the point of intersection of the lines whose equations are x + 3y = 18 and 2x + y =
11.
(s,3)
c) (2, 3)
D) (3, 2)
' }
?
16. Suppose the feasible region has four comers, at these points: (0, 0), (8, 0), (0,1.2), and
formulae is the profit maximized, producing a mix of
(4, 8). For which of these
products?
A) $5x + $2y
@ $2x + SSy
C) Sx-$y
D) $2x - $y
17. Consider the feasible region identified by the inequalities below.
x_> 0; y___ 0; x+y_<4; x +3y< 6
Which point is not a comer of the region?
A) (0, 2)
\,ÿ (0, 4)
(3,1)
D) (4, O)
18. The Sterling Milk Company has three plants located throughout a state with production capacity 50, 75 and 25
gallons. Each day the firm must furnish its four retail shops R1, R2, R3, & R4 with at least 20, 20, 50, and 60 gallons
respectively.
%ÿ@
Retail Shops
Plant
P3
R2
R3
R4
1
2
3
4
131
P1
P2
R1
LzJ
ZI
ZI£
I Demand
3LzJ
LAJ
20
Supply
7Lÿ
6Lÿ
8Lÿ
121
191
121
5O
75
25
150
Page 5
19. Luminous lamps have three factories - F1, F2, and F3 with production capacity 30, 50, and 20 units per week
respectively. These units are to be shipped to four warehouses W1, Wz, W3, and W4 with requirement of 20, 40, 30, and 10
units per week respectively. The transportation costs per unit between factories and warehouses are given below:
Warehouse
I
WI
Factory
1
2
W3
W4
3
4
30
F1
F2
II
5O
F3
III
20
2O
Demand
4O
3O
Solution:
20.
Apply the Northwest Corner Rule to the following tableau.
T
Supply
I;
ÿ'
f
4 5u:,plies
J
ii
B,._, ma>ld.ÿ
Determine the cost associated with the solution you found.
Page 6
10
100