Deck 7: Linear Programming

Question 1

Graph the linear inequality.

- $2 x+y \leq-4$

A)
B)
C)
D)

Answer 1

Question 2

Graph the linear inequality.

- $x+2 y \geq-1$

A)
B)
C)
D)

Answer 2

Question 3

Graph the linear inequality.

- $y \leq-x+7$

A)
B)
C)
D)

Answer 3

Question 4

Graph the linear inequality.

- $2 x+5 y \leq 10$

A)
B)
C)
D)

Question 5

Graph the linear inequality.

- $-3 x-5 y \leq 15$

A)
B)
C)
D)

Question 6

Graph the linear inequality.

- $2 x+4 y \geq-8$

A)
B)
C)
D)

Question 7

Graph the linear inequality.

- $y<x+2$

A)
B)
C)
D)

Question 8

Graph the linear inequality.

- $x+y<-4$

A)
B)
C)
D)

Question 9

Graph the linear inequality.

- $x-y<6$

A)
B)
C)
D)

Question 10

Graph the linear inequality.

- $y \geq 5$

A)
B)
C)
D)

Question 11

Graph the feasible region for the system of inequalities.

- $2 x+y \leq 4$
$x-1 \geq 0$

A)
B)
C)
D)

Question 12

Graph the feasible region for the system of inequalities.

- $2 x+y \geq 4$
$\mathrm{x}-1 \geq 0$

A)
B)
C)
D)

Question 13

Graph the feasible region for the system of inequalities.

- $2 x+y \leq 4$
$y-1 \leq 0$

A)
B)
C)
D)

Question 14

Graph the feasible region for the system of inequalities.

- $3 x-2 y \leq 6$
$\mathrm{x}-1 \geq 0$

A)
B)
C)
D)

Question 15

Graph the feasible region for the system of inequalities.

- $3 x-2 y \geq-6$
$x - 1 < 0$

A)
B)
C)
D)

Question 16

Graph the feasible region for the system of inequalities.

- $3 x+2 y \leq-6$
$x-1 \geq 0$

A)
B)
C)
D)

Question 17

Graph the feasible region for the system of inequalities.

- $x+2 y \leq 2$
$x+y \geq 0$

A)
B)
C)
D)

Question 18

Graph the feasible region for the system of inequalities.

- $x-2 y \leq 2$
$x+y \leq 0$

A)
B)
C)
D)

Question 19

Graph the feasible region for the system of inequalities.

- $x+2 y \geq 2$
$x-y \leq 0$

A)
B)
C)
D)

Question 20

Graph the feasible region for the system of inequalities.

- $6 y-x \leq 8$
$-y+3 x \leq 6$
$\mathrm{x} \leq 0$

A)

B)
C)
D)

Question 21

Graph the feasible region for the system of inequalities.

- $2 y+x \geq-2$
$\mathrm{y}+3 \mathrm{x} \leq 9$
$y \leq 0$
$x \geq 0$

A)
B)
C)
D)

Question 22

Graph the feasible region for the system of inequalities.

- $3 y+x \geq-6$
$y+2 x \leq 8$
$y \leq 0$
$x \geq 0$

A)
B)
C)
D)

Question 23

Graph the feasible region for the system of inequalities.

- $4 y+x \geq-2$
$y+2 x \leq 10$
$4 y \leq 10 x+40$
$\mathrm{y} \geq 0$

A)
B)
C)
D)

Question 24

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production.

-Use $x$ -for the number of chairs and $y$ for the number of tables made per week. The number of work hours a yailable for construction and finishing is fixed.

A) $2 x+3 y \leq 36$
$2 x+2 y \leq 28$
$x \geq 0$
$y \geq 0$
B) $2 x+3 y \geq 28$
$2 x+2 y \geq 36$
$x \geq 0$
$y \geq 0$
C) $2 x+3 y \geq 36$
$2 x+2 y \geq 28$
$x \geq 0$
$y \geq 0$
D) $2 x+3 y \leq 28$
$2 x+2 y \leq 36$
$x \geq 0$
$y \geq 0$

Question 25

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production.

-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.

A) $2 x+4 y+48 \leq 0$
$2 x+3 y+42 \leq 0$
B) $2 x+4 y \geq 48$
$2 x+3 y \geq 42$
$x \geq 0$
$\mathrm{y} \geq 0$
C) $2 x+4 y \leq 48$
$2 x+3 y \leq 42$
D) $2 x+4 y \leq 48$
$2 x+3 y \leq 42$
$x \geq 0$
$y \geq 0$

Question 26

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production.

-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.

A) $x+3 y \leq 27$
$x+2 y \leq 20$
$x \geq 0$
$y \geq 0$
B) $x+3 y \geq 0$
$x+2 y \geq 0$
$x \leq 27$
$y \leq 20$
C) $x+3 y \geq 27$
$x+2 y \geq 20$
D) $x+y \geq 36$
$3 x+2 y \geq 0$
$27 x+20 y \geq 0$

Question 27

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production.

-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.

A) $3 x+2 y \geq 0$
$2 x+4 y \geq 0$
$x \leq 30$
$\mathrm{y} \leq 24$
B) $x \leq 5$
$y \leq 6$
C) $3 x+2 y \leq 30$
$2 x+4 y \leq 24$
$x \geq 0$
$y \geq 0$
D) $x \leq 6$
$\mathrm{y} \leq 4$

Question 28

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production.

-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.

A) $3 x+4 y \leq 56$
$2 x+2 y \leq 56$
$x \geq 0$
$x \geq 0$
B) $3 x+2 y \leq 56$
$2 x+4 y \leq 56$
C) $3 x+4 y \leq 36$
$2 x+2 y \leq 20$
$\mathrm{x} \geq 0$
$\mathrm{y} \geq 0$
D) $3 x+2 y \leq 36$
$2 x+4 y \leq 20$

Question 29

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production.

-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.

A) $3 x+4 y \leq 48$
$3 x+3 y \leq 42$
$x \geq 0$
$y \geq 0$
B) $3 x+4 y \leq 48$
$3 x+3 y \leq 42$
$x \leq 0 \quad$
$y \leq 0 \quad$
C) $3 x+3 y \leq 48$
$4 x+3 y \leq 42$
$x \geq 0$
$y \geq 0$
D) $4 x+3 y \leq 48$
$3 x+3 y \leq 42$
$x \geq 0$
$y \geq 0$

Question 30

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production.

-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.

A) $2 x+5 y \leq 20$
$2 x+2 y \leq 12$
$x \leq 0 \quad$
$y \leq 0 \quad$
B) $2 x+5 y \leq 20$
$2 x+2 y \leq 12$
$x \geq 0$
$y \geq 0$
C) $2 x+5 y \leq 20$
$2 x+2 y \leq 12$
$\mathrm{x}+\mathrm{y} \geq 0$
D) $2 x+5 y \leq 20$
$2 x+2 y \leq 12$

Question 31

A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a givenweek. Use the table to find the system of inequalities that describes the manufacturer's weekly production.

-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.

A) $3 x+5 y \leq 45$
$3 x+3 y \leq 30$
$x \leq 0$
$y \leq 0$
B) $5 x+3 y \leq 30$
$3 x+3 y \leq 45$
$x \geq 0$
$y \geq 0$
C) $3 x+5 y \leq 45$
$3 x+3 y \leq 30$
$x \geq 0$
$y \geq 0$
D) $5 x+3 y \leq 45$
$3 x+3 y \leq 30$
$x \geq 0$
$\mathrm{y} \geq 0$

Question 32

Find the value(s) of the function on the given feasible region.

-Find the maximum and minimum of $z=20 x+5 y$ .

A) 225,15
B) 225,200
C) 200,15
D) 25,15

Question 33

Find the value(s) of the function on the given feasible region.

-Find the minimum of $z=23 x+14 y+19$ .

A) 42
B) 56
C) 19
D) 33

Question 34

Find the value(s) of the function on the given feasible region.

-Find the maximum and minimum of $z=8 x-9 y$ .

A) $-54,0$
B) $40,-54$
C) $-35,-54$
D) 40,0

Question 35

Find the value(s) of the function on the given feasible region.

-Find the maximum and minimum of $z=6 x+6 y$ .

A) 36,30
B) $-24,-42$
C) 42,24
D) 60,24

Question 36

Find the value(s) of the function on the given feasible region.

-Find the minimum of $z=14 x+10 y$ .

A) 29
B) 39
C) 15
D) 10

Question 37

Use graphical methods to solve the linear programming problem.

-Maximize $z = 6x + 7y$
Subject to: $2 x+3 y \leq 12$
$2 x+ y \leq 8$
$x \geq 0$
$y \geq 0$

A) Maximum of 52 when $x=4$ and $y=4$
B) Maximum of 32 when $x=2$ and $y=3$
C) Maximum of 24 when $x=4$ and $y=0$
D) Maximum of 32 when $x=3$ and $y=2$

Question 38

Use graphical methods to solve the linear programming problem.

-Maximize $\mathrm{z}=8 \mathrm{x}+12 \mathrm{y}$
Subject to:
$40 x+80 y \leq 560$
$6 x+8 y \leq 72$
$x \geq 0$
$y \geq 0$

A) Maximum of 120 when $x=3$ and $y=8$
B) Maximum of 92 when $x=4$ and $y=5$
C) Maximum of 96 when $x=9$ and $y=2$
D) Maximum of 100 when $x=8$ and $y=3$

Question 39

Use graphical methods to solve the linear programming problem.

-Minimize $\quad z=0.18 x+0.12 y$
Subject to: $\quad 2 x+6 y \geq 30$
$4 x+2 y \geq 20$
$x \geq 0$
$y \geq 0$

A) Minimum of 1.08 when $x=4$ and $y=3$
B) Minimum of 1.86 when $x=9$ and $y=2$
C) Minimum of 1.2 when $x=4$ and $y=4$
D) Minimum of 1.02 when $x=3$ and $y=4$

Question 40

Use graphical methods to solve the linear programming problem.

-Maximize $\mathrm{z}=2 \mathrm{x}+5 \mathrm{y}$
Subject to: $\quad 3 x+2 y \leq 6$
$-2 x+4 y \leq 8$
$x \geq 0$
$y \geq 0$

A) Maximum of $\frac{49}{4}$ when $\mathrm{x}=\frac{1}{2}$ and $\mathrm{y}=\frac{9}{4}$
B) Maximum of 19 when $x=2$ and $y=3$
C) Maximum of 10 when $x=0$ and $y=2$
D) Maximum of $\frac{34}{3}$ when $x=\frac{2}{3}$ and $y=2$

Question 41

Use graphical methods to solve the linear programming problem.

-Minimize $z=2 x+4 y$
Subject to:
$x+2 y \geq 10$
$3 x+y \geq 10$
$x \geq 0$
$y \geq 0$

A) Minimum of 20 when $x=10$ and $y=0$
B) Minimum of 20 when $x=2$ and $y=4$
C) Minimum of 20 when $\mathrm{x}=2$ and $\mathrm{y}=4$ , as well as when $\mathrm{x}=10$ and $\mathrm{y}=0$ , and all points in between
D) Minimum of 0 when $x=0$ and $y=0$

Question 42

Use graphical methods to solve the linear programming problem.

-Minimize $z = 6x + 8y$
Subject to: $2x+4 y \geq 12$
$2 x+y \geq 8$
$x \geq 0$
$y \geq 0$

A) Minimum of 26 when $x=3$ and $y=1$
B) Minimum of 36 when $x=6$ and $y=0$
C) Minimum of $\frac{92}{3}$ when $x=\frac{10}{3}$ and $y=\frac{4}{3}$
D) Minimum of 0 when $x=0$ and $y=0$

Question 43

Use graphical methods to solve the linear programming problem.

-Minimize $z=4 x+5 y$
Subject to: $\quad 2 x-4 y \leq 10$
$2 x+y \geq 15$
$x \geq 0$
$y \geq 0$

A) Minimum of 33 when $x=7$ and $y=1$
B) Minimum of 39 when $x=1$ and $y=7$
C) Minimum of 20 when $x=5$ and $y=0$
D) Minimum of 75 when $x=0$ and $y=15$

Question 44

Find the value(s) of the function, subject to the system of inequalities.

-Find the maximum and minimum of $P=24 x+21 y$ subject to:
$0 \leq x \leq 10,0 \leq y \leq 5,3 x+2 y \geq 6$ .

A) 345,63
B) 105,63
C) 240,63
D) 345,240

Question 45

Find the value(s) of the function, subject to the system of inequalities.

-Find the minimum of $P=16 x+7 y+23$ subject to:
$x \geq 0, y \geq 0, x+y \geq 1$ .

A) 46
B) 39
C) 30
D) 23

Question 46

Find the value(s) of the function, subject to the system of inequalities.

-Find the maximum and minimum of $P=9 x-12 y$ subject to:
$0 \leq x \leq 5,0 \leq y \leq 8,4 x+5 y \leq 30$ , and $4 x+3 y \leq 20$ .

A) $-72,0$
B) 45,0
C) $45,-72$
D) $-48.75,-72$

Question 47

Find the value(s) of the function, subject to the system of inequalities.

-Find the maximum and minimum of $Z=19 x+12 y$ subject to:
$0 \leq x \leq 10,0 \leq y \leq 5,3 x+2 y \geq 6$ .

A) 190,36
B) 60,36
C) 250,190
D) 250,36

Question 48

Find the value(s) of the function, subject to the system of inequalities.

-Find the minimum of $Z=16 x+15 y+19$ subject to:
$x \geq 0, y \geq 0, x+y \geq 1$ .

A) 35
B) 50
C) 34
D) 19

Question 49

Find the value(s) of the function, subject to the system of inequalities.

-Find the maximum and minimum of $Z=9 x-18 y$ subject to:
$0 \leq x \leq 5,0 \leq y \leq 8,4 x+5 y \leq 30$ , and $4 x+3 y \leq 20$ .

A) 45,0
B) $-78.75,-108$
C) $-108,0$
D) $45,-108$

Question 50

State the linear programming problem in mathematical terms, identifying the objective function and the constraints.

-A firm makes products $A$ and B. Product A takes 3 hours each on machine $L$ and machine M; product B takes 3 hours on $L$ and 2 hours on M. Machine $L$ can be used for 13 hours and M for 8 hours. Profit on product $A$ is $\$ 7$ and $\$ 10$ on B. Maximize profit.

A) Maximize $7 \mathrm{~A}+10 \mathrm{~B}$
Subject to: $3 \mathrm{~A}+3 \mathrm{~B} \geq 13$
$2 \mathrm{~A}+3 \mathrm{~B} \geq 8$
$\mathrm{A}, \mathrm{B} \leq 0$ .
B) Maximize $7 \mathrm{~A}+10 \mathrm{~B}$
Subject to: $3 \mathrm{~A}+3 \mathrm{~B} \leq 13$
$2 \mathrm{~A}+3 \mathrm{~B} \leq 8$
$\mathrm{A}, \mathrm{B} \geq 0$ .
C) Maximize $7 \mathrm{~A}+10 \mathrm{~B}$
Subject to: $3 \mathrm{~A}+3 \mathrm{~B} \leq 13$
$3 \mathrm{~A}+2 \mathrm{~B} \leq 8$
$\mathrm{A}, \mathrm{B} \geq 0$ .
D) Maximize $10 \mathrm{~A}+7 \mathrm{~B}$
Subject to: $3 A+2 B \leq 13$
$3 \mathrm{~A}+3 \mathrm{~B} \leq 8$
$\mathrm{A}, \mathrm{B} \geq 0$ .

Question 51

State the linear programming problem in mathematical terms, identifying the objective function and the constraints.

-A car repair shop blends oil from two suppliers. Supplier I can supply at most 45 gal with $3.9 \%$ detergent. Supplier II can supply at most $67 \mathrm{gal}$ with $3.3 \%$ detergent. How much can be ordered from each to get at most 100 gal of oil with maximum detergent?

A) Maximize $0.033 x+0.039 y$
Subject to: $x \leq 45$
$y \leq 67$
$x+y \leq 100$ .
B) Maximize $45 x+67 y$
Subject to: $x \geq 45$
$y \geq 67$
$0)039 x+0.033 y \geq 100$ .
C) Maximize $45 x+67 y$
Subject to: $x \leq 45$
$\mathrm{y} \leq 67$
$0)039 x+0.033 y \leq 100$ .
D) Maximize $0.039 x+0.033 y$
Subject to: $0 \leq x \leq 45$
$0 \leq \mathrm{y} \leq 67$
$x+y \leq 100$ .

Question 52

State the linear programming problem in mathematical terms, identifying the objective function and the constraints.

-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 $\$ 3 / \mathrm{bag}$ . Feed ty pe II provides 2 protein and 5 fat units at $\$ 2 / \mathrm{bag}$ . Which mixture fills the needs at minimum cost?

A) Minimize $2 x+3 y$
Subject to: $6 x+2 y \geq 10$
$2 x+5 y \geq 8$
$x, y \geq 0$ .
B) Minimize $3 x+2 y$
Subject to: $6 x+2 y \leq 8$
$2 x+5 y \leq 10$
$\mathrm{x}, \mathrm{y} \leq 0$ .
C) Minimize $3 x+2 y$
Subject to: $6 x+2 y \geq 10$
$2 x+5 y \geq 8$
$x, y \geq 0$ .
D) Minimize $3 x+2 y$
Subject to: $6 x+2 y \geq 8$
$2 x+5 y \geq 10$
$\mathrm{x}, \mathrm{y} \geq 0$ .

Question 53

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring.

-How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 30$ and on an SST ring is $\$ 40$ ?

A) 12 VIP and 12 SST
B) 8 VIP and 16 SST
C)0 VIP and 24 SST
D) 16 VIP and 8 SST

Question 54

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring.

-How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 30$ and on an SST ring is $\$ 60$ ?

A) 16 VIP and 8 SST
B) 8 VIP and 16 SST
C) 0 VIP and 24 SST
D) 12 VIP and 12 SST

Question 55

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring.

-How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 50$ and on an SST ring is $\$ 10$ ?

A) 20 VIP and 4 SST
B) $24 \mathrm{VIP}$ and 4 SST
C) 24 VIP and 0 SST
D) 20 VIP and 0 SST

Question 56

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring.

-How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 40$ and on an SST ring is $\$ 35$ ?

A) 16 VIP and 8 SST
B) 18 VIP and 6 SST
C) 12 VIP and 12 SST
D) 14 VIP and 10 SST

Question 57

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring.

-How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 40$ and on an SST ring is $\$ 30$ ?

A) 12 VIP and 12 SST
B) 10 VIP and 14 SST
C) 14 VIP and 14 SST
D) 14 VIP and 10 SST

Question 58

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring.

-How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 60$ and on an SST ring is $\$ 20$ ?

A) 24 VIP and 4 SST
B) 20 VIP and 4 SST
C) 24 VIP and 0 SST
D) 20 VIP and 0 SST

Question 59

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring.

-How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 20$ and on an SST ring is $\$ 50$ ?

A) 12 VIP and 12 SST
B) 0 VIP and 20 SST
C) 4 VIP and 20 SST
D) 0 VIP and 24 SST

Question 60

The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24rings each day using up to 60 total man hours of labor. It takes 3 man hours to make one VIP ring, versus 2 man hoursto make one SST ring.

-How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $\$ 50$ and on an SST ring is $\$ 40$ ?

A) 12 VIP and 12 SST
B) 14 VIP and 10 SST
C) 20 VIP and 4 SST
D) 10 VIP and 14 SST

Question 61

Provide an appropriate response.

-To determine the shading when graphing $6 x+8 y \geq 0$ , the point $(0,0)$ would make a good test point. ?

Question 62

Provide an appropriate response.

-The graph of $a x+b y \geq c$ is always shaded above the line $a x+b y=c$ , regardless of any nonzero choices of $a, b$ , and $c$ .

Question 63

Provide an appropriate response.

-The feasible region of a set of two inequalities must always be unbounded.

Question 64

Provide an appropriate response.

-It is possible to have a system of linear inequalities with a feasible region that includes more than one enclosed region.

Question 65

Provide an appropriate response.

-If a system has four inequalities, the number of corner points of the feasible region must be ?

A) exactly three
B) at least three, but not more than four
C) at least one, but not more than four
D) exactly four

Question 66

Provide an appropriate response.

-Describe the feasible region of $x+y \geq 9$ and $x+y \leq-6$ .

A) Two bounded regions
B) A bounded region
C) An empty region
D) An unbounded region

Question 67

Provide an appropriate response.

-Describe the feasible region of $x+y \leq 17, x+2 y \geq 8$ , and $2 x+y \geq 6$ .

A) Two bounded regions
B) An empty region
C) A bounded region
D) An unbounded region

Question 68

Provide an appropriate response.

-If the inequalities $x \geq 0$ and $y \geq 0$ are included in a system, the feasibility region is restricted to the axes and which quadrant?

A) Fourth
B) First
C) Second
D) It is not restricted.

Question 69

Provide an appropriate response.

-If a system of inequalities includes $x \leq 1$ , then the feasibility region is restricted to what?

A) The region right of and including $x=1$
B) The region left of and including $x=-1$
C) The region left of and including $x=1$
D) The region right of and including $x=-1$

Question 70

Provide an appropriate response.

-What is the least number of inequalities needed to produce a closed region?

A) 1
B) 2
C) 4
D) 3

Question 71

Provide an appropriate response.

-Is it possible to have a bounded feasible region that does not optimize an objective function?

Question 72

Provide an appropriate response.

-Is it possible that the feasible region of a linear program include more than one distinct area?

Question 73

Provide an appropriate response.

-Does a linear program with at least three constraints always have a closed feasible region?

Question 74

Provide an appropriate response.

-Consider a linear program with an objective function for profit. Thinking of isoprofit lines, if the objective function is evaluated at the corner points of polygon $A B C D$ , and $p(A)=10, p(B)=20$ , and $p(C)=5$ , is it safe to assume that $p(D)$ is not the corner point at which the profit is maximized?

Question 75

Provide an appropriate response.

-A linear program is defined with constraints $2 x+2 y \geq 4,7 x+9 y \geq 0, x \geq 0$ , and $y \geq 0$ . Is the feasibility region bounded, unbounded, or empty?

A) Bounded
B) Unbounded
C) Empty

Question 76

Write the word or phrase that best completes each statement or answers thequestion.
-Explain how you decide which half-plane to shade when you are graphing an inequality.

Question 77

Write the word or phrase that best completes each statement or answers thequestion.
-Explain why the graphing method is not satisfactory for solving a linear programming problem with 3 variables.

Question 78

Write the word or phrase that best completes each statement or answers thequestion.
-Explain why the solution to a linear programming problem always occurs at a corner point of the feasible region.

Question 79

Write the word or phrase that best completes each statement or answers thequestion.
-Can there be more than one point in the feasible region where the maximum or minimum occurs? Explain.

Question 80

Write the word or phrase that best completes each statement or answers thequestion.
-In an unbounded region, will there always be a solution?