1 (5 points) Solve the following system of linear equations using the substitution method: 3x2y=18 5x+10y=10 Express answer as an ordered pair. Question 7 (7.5 points) A moving company charges a flat rate of $150, and an additional $5 for each box. A delivery service would charge $20 for each box. After how many boxes would it be cheaper to use the moving company? Question 8 (7.5 points) In the graph above, which set of corner points defines the feasible region for the following system of linear inequalities: x+3y18 2x+y16 x0 y0 Question 8 options: (0, 6) ; (0, 16) ; (6, 4) (Region II) (0, 6) ; (0, 0) ; (8, 0) ; (6, 4) (Region III) (0,16) ; (6, 4) ; (18, 0) (Region I) (6, 4) ; (8, 0) ; (18, 0) (Region IV) Question 9 (7.5 points) In the graph above, which set of corner points defines the feasible region for the following system of linear inequalities: 2x+y16 x+3y18 x0 y0 Question 9 options: (0, 6) ; (0, 16) ; (6, 4) (Region II) (0, 6) ; (0, 0) ; (8, 0) ; (6, 4) (Region III) (6, 4) ; (8, 0) ; (18, 0) (Region IV) (0,16) ; (6, 4) ; (18, 0) (Region I) Question 10 (7.5 points) In the graph above, which set of corner points defines the feasible region for the following system of linear inequalities: 2x+y16 x+3y18 x0 y0 Question 10 options: (0,16) ; (6, 4) ; (18, 0) (Region I) (0, 6) ; (0, 16) ; (6, 4) (Region II) (0, 6) ; (0, 0) ; (8, 0) ; (6, 4) (6, 4) ; (8, 0) ; (18, 0) Question 11 (5 points) (Region III) (Region IV) In the graph above, the UNBOUNDED feasible region is defined by which system of linear inequalities? Question 11 options: x+3y18 2x+y16 x0 y0 x+3y18 2x+y16 x0 y0 x+3y18 2x+y16 x0 y0 x+3y18 2x+y16 x0 y0 Question 12 (7.5 points) Question 12 options: Solve using the graphical method. Choose your variables, identify the objective function and the constraints, graph the constraints, shade the feasibility region, identify all corner points, and determine the solution that optimizes the objective function. Use this information to answer the following 8-part question: A small company manufactures two types of radios- regular and short-wave. The manufacturing of each radio requires two operations: Assembly and Finishing. The regular radios require 1 hour of Assembly and 3 hours of Finishing. The short-wave radios require 3 hours of Assembly and 1 hour of Finishing. The total labor-hours available per week in the Assembly division is 60, and in the Finishing division, 60. A profit of $50 is realized for every regular radio, and $75 for every short-wave radio. Management wants to determine the number of each type of radio to produce so that profit can be maximized. (i) Which variable should x define? (Enter letter for correct answer in the blank) a. number of regular radios produced b. number of labor-hours needed for assembly c. total number of radios to produce in order to maximize profit d. number of labor-hours needed for finishing (ii) Which variable should y define? (Enter letter for correct answer in the blank) a. total number of radios to produce in order to maximize profit b. number of short-wave radios produced c. number of labor-hours needed for assembly d. number of labor-hours needed for finishing (iii) Which of the following correctly defines the constraint on labor-hours for radio assembly? (Enter letter for correct answer in the blank) a. 3x+y60 b. x+3y60 c. x+3y60 d. 3x+y60 (iv) Which of the following correctly defines the constraint on labor-hours needed for radio finishing? (Enter letter for correct answer in the blank) a. 3x+y60 b. x+3y60 c. x+3y60 d. 3x+y60 (v) Which of the following correctly defines the objective function? (Enter letter for correct answer in the blank) a. P=60x+60y b. P=75x+50y c. P=50x+75y d. P=300x+4500y{ (vi) Which of the following sets of corner points correctly defines the feasible region for this system of linear inequalities? (Enter letter for correct answer in the blank) a. (0,20) ; (0,60) ; (15,15) b. (0,20) ; (0,0) ; (20,0) ; (15,15) c. (0,60) ; (15,15) ; (60,0) d. (15,15) ; (20,0) ; (60,0) (vii) Based on your determination of the feasible region for this business process, how many radios of each type should be produced in order to maximize profit? (Enter letter for correct answer in the blank) a. 0 regular radios and 20 shortwave radios b. 20 regular radios and 0 shortwave radios c. 15 regular radios and 15 shortwave radios d. 0 regular radios and 60 shortwave radios (viii) Which of the following is the correct value for the maximum total profit made from producing the optimum number of each type of radio? a. P=$4500b. P=$3000c. P=$1500d. P=$1875 Question 13 (7.5 points) Question 13 options: Solve using the graphical method. Choose your variables, identify the objective function and the constraints, graph the constraints, shade the feasibility region, identify all corner points, and determine the solution that optimizes the objective function. Use this information to answer the following 8-part question: A company produces two types of shoes - casual, and athletic - at its two factories, Factory I and Factory II. Daily production at each factory for number of pairs of each type of shoe is listed below: Casual Athletic Factory I 100 300 Factory II 200 100 The company must produce at least 8000 pairs of casual shoes, and 9000 pairs of athletic shoes. The cost of operating Factory I is $1500 per day and the cost of operating Factory II is $2000. Management needs to determine the number of days each factory needs to operate to meet production goals at minimum cost. (i) Which variable should x define? (Enter letter for correct answer in the blank) a. number of pairs of athletic shoes produced b. number of days Factory I operates c. number of pairs of casual shoes produced d. cost to produce a pair of athletic shoes (ii) Which variable should y define? (Enter letter for correct answer in the blank) a. number of pairs of athletic shoes produced b. cost to produce a pair of casual shoes c. number of pairs of casual shoes produced d. number of days Factory II operates (iii) Which of the following correctly defines the constraint on total daily production of pairs of casual shoes? (Enter letter for correct answer in the blank) a. 200x+100y8000 b. 100x+200y8000 c. 200x+100y8000 d. 100x+200y8000 (iv) Which of the following correctly defines the constraint on total daily production of pairs of athletic shoes? (Enter letter for correct answer in the blank) a. 300x+100y9000 b. 100x+300y9000 c. 300x+100y9000 d. 100x+300y9000"} (v) Which of the following correctly defines the objective function? (Enter letter for correct answer in the blank) a. C=8000x+9000y b. C=9000x+8000y c. C=1500x+2000y d. C=2000x+1500y (vi) Which of the following sets of corner points correctly defines the feasible region for this system of linear inequalities? (Enter letter for correct answer in the blank) a. (0, 0) ; (40, 0) ; (20, 30) ; (30, 0) b. (0, 40) ; (0, 90) ; (20, 30) c. (0, 90) ; (20, 30) ; (80, 0) d. (20, 30) ; (30, 0) ; (80, 0) (vii) Based on your determination of the feasible region for this business process, how many days should each factory operate to meet production goals at minimum cost? (Enter letter for correct answer in the blank) a. 30 days for Factory I and 0 days for Factory II b. 20 days for Factory I and 30 days for Factory II c. 0 days for Factory I and 40 days for Factory II d. None of these answers are correct (viii) Which of the following is the correct value for the minimum cost to meet production goals for both types of shoes? a. C = $45000b. C = $80000c. C = $90000d. C = $120000 Question 14 (7.5 points) Question 14 options: Solve using the graphical method. Choose your variables, identify the objective function and the constraints, graph the constraints, shade the feasibility region, identify all corner points, and determine the solution that optimizes the objective function. Use this information to answer the following 8-part question: Sunnydale Farms has a total of 240 acres of cropland. The farm owner wants to plant this acreage in corn and oats. An acre of corn brings $40 in profit, and an acre of oats gets $30 profit. A total of 320 labor-hours to raise the crops is available. Each acre of corn needs 2 labor-hours, and each acre of oats needs 1 labor-hour. The farm owner wants to optimize the planting of the 240 acres to make maximum profit. (i) Which variable should x define? (Enter letter for correct answer in the blank) a. total amount of profit made from planting corn b. number of labor-hours for optimum oats planting c. number of labor-hours for optimum corn planting d. number of acres of corn planted (ii) Which variable should y define? (Enter letter for correct answer in the blank) a. number of acres of oats planted b. number of labor-hours for optimum oats planting c. number of labor-hours for optimum corn planting d. total amount of profit made from planting oats (iii) Which of the following correctly defines the constraint on total acres of cropland available for planting? (Enter letter for correct answer in the blank) a. 40x+30y240 b. 2x+y320 c. x+y240 d. 40x+30y320 (iv) Which of the following correctly defines the constraint on labor-hours available for farming? (Enter letter for correct answer in the blank) a. x+y240 b. x+y320 c. 2x+y240 d. 2x+y320 (v) Which of the following correctly defines the objective function? (Enter letter for correct answer in the blank) a. P=x+y b. P=40x+30y c. P=2x+y d. P=320x240y (vi) Which of the following sets of corner points correctly defines the feasible region for this system of linear inequalities? (Enter letter for correct answer in the blank) a. (0, 320) ; (80, 160) ; (240, 0) b. (0, 240) ; (80, 160) ; (160, 0) ; (0, 0) c. (0, 240) ; (0, 320) ; (80, 160) d. (160, 0) ; (240, 0) ; (80, 160) (vii) Based on your determination of the feasible region for this business process, how many acres of corn and of oats should be planted to maximize profit? (Enter letter for correct answer in the blank) a. 160 acres of corn and 0 acres of oats b. 240 acres of corn and 0 acres of oats c. 80 acres of corn and 160 acres of oats d. None of these answers are correct (viii) Which of the following is the correct value for the amount of total maximum profit from raising the optimum acres of the two crops? a. $8000b. $9600c. $7200d. $6400 Question 15 (7.5 points) Question 15 options: Solve using the graphical method. Choose your variables, identify the objective function and the constraints, graph the constraints, shade the feasibility region, identify all corner points, and determine the solution that optimizes the objective function. Use this information to answer the following 8-part question: A city council voted to conduct a study on inner-city community problems using sociologists and research assistants from UMUC. Allocation of time and costs per week are given in the following table: Labor Labor hours hours - research Sociologist assistant Fieldwork 10 30 MINIMUM labor hours needed per week 180 Research center 30 10 Costs per week $500 $300 140 (i) Which variable should x define? (Enter letter for correct answer in the blank) a. total amount of labor hours needed for sociologists b. number of sociologists needed for the study c. total number of labor-hours needed for research assistants d. total number of study team members needed (ii) Which variable should y define? (Enter letter for correct answer in the blank) a. total number of study team members needed b. total number of labor-hours needed for research assistants c. total number of labor-hours needed for sociologists d. number of research assistants needed for the study (iii) Which of the following correctly defines the constraint on number of labor hours for fieldwork? (Enter letter for correct answer in the blank) a. 30x+10y140 b. 30x+10y140 c. 10x+30y180 d. 10x+30y180 (iv) Which of the following correctly defines the constraint on labor-hours needed at the research center? (Enter letter for correct answer in the blank) a. 30x+10y140 b. 30x+10y140 c. 10x+30y180 d. 10x+30y180 (v) Which of the following correctly defines the objective function? (Enter letter for correct answer in the blank) a. C=10x+30y b. C=30x+10y c. C=500x+300y d. C=300x+500y (vi) Which of the following sets of corner points correctly defines the feasible region for this system of linear inequalities? (Enter letter for correct answer in the blank) a. (0, 14) ; (0, 6) ; (3, 5) b. (0, 14) ; (3, 5) ; (18, 0) c. (0, 6) ; (3, 5) ; (18, 0) d. (0, 6) ; (3, 5) ; (5, 0) ; (0, 0) (vii) Based on your determination of the feasible region for this business process, how many sociologists and how many research assistants should be hired to complete this study for minimum cost? (Enter letter for correct answer in the blank) a. 3 sociologists and 5 research assistants b. 0 sociologists and 14 research assistants c. 18 sociologists and 0 research assistants d. None of these answers are correct (viii) Which of the following is the correct value for the minimum cost to complete this study? a. C=$2500b. C=$3000c. C=$4200d. C=$9000