Transcription of 3-4 Study Guide and Intervention
1 Glencoe/McGraw-Hill138 Glencoe Algebra 2 Real-World ProblemsWhen solving linear programmingproblems, use thefollowing a system of the system of the coordinates of the vertices of the feasible an expression to be maximized or the coordinates of the vertices in the the greatest or least result to answer the painter has exactly 32 units of yellow dye and 54 units of greendye. He plans to mix as many gallons as possible of color A and color B. Eachgallon of color A requires 4 units of yellow dye and 1 unit of green dye.
2 Eachgallon of color B requires 1 unit of yellow dye and 6 units of green dye. Find themaximum number of gallons he can 1 Define the number of gallons of color A madey5the number of gallons of color B madeStep 2 Write a system of the number of gallons made cannot benegative,x$0 and y$ are 32 units of yellow dye; each gallon of color A requires 4 units, and each gallon of color B requires 1 4x1y# for the green dye,x16y# 3 and 4 Graph the system of inequalities and find the coordinates of the vertices of the feasible vertices of the feasible region are (0, 0), (0, 9), (6, 8), and (8, 0).
3 Steps 5 7 Find the maximum number of gallons,x1y, that he can maximum number of gallons the painter can make is 14,6 gallons of color A and 8 gallons of color delicatessen has 8 pounds of plain sausage and 10 pounds of garlic-flavoredsausage. The deli wants to make as much bratwurst as possible. Each pound of bratwurst requires pound of plain sausage and pound of garlic-flavored the maximum number of pounds of bratwurst that can be A can produce 30 steering wheels per hour at a cost of $16per hour. Machine B can produce 40 steering wheels per hour at a cost of $22 per least 360 steering wheels must be made in each 8-hour shift.
4 What is the least costinvolved in making 360 steering wheels in one shift?$1942}31}43}4(x,y)x1yf(x,y)(0, 0)0 100(0, 9)0 199(6, 8)6 1814(8, 0)8 108 Color A (gallons)Color B (gallons)5 10 15 20 25 3035 40 45 50 550403530252015105(6, 8)(8, 0)(0, 9) Study Guide and Intervention (continued)Linear ProgrammingNAME _____ DATE_____ PERIOD _____3-43-4 ExampleExampleExercisesExercisesSkills PracticeLinear ProgrammingNAME _____ DATE _____ PERIOD _____3-43-4 Glencoe/McGraw-Hill139 Glencoe Algebra 2 Lesson 3-4 Graph each system of inequalities.
5 Name the coordinates of the vertices of thefeasible region. Find the maximum and minimum values of the given function forthis $ $ $0x#5y#6y$0y$1y$x22y#7 2xy#4f(x,y) 5x2yf(x,y) 53x1yf(x,y) 5x1ymax.: 9, min.: 3max.: 2, min.: 25max.: 21, min.: $ # $ 2x22x1y#6y$6 2xy$3x12f(x,y) 5x12yy#6y#x14f(x,y) 54x13yf(x,y) 5 23x15ymax.: 13, no max., min.: 20max.: 22, min.: backpack manufacturer produces an internal frame pack and anexternal frame pack. Let xrepresent the number of internal frame packs produced inone hour and let yrepresent the number of external frame packs produced in one the inequalities x13y#18, 2x1y#16,x$0, and y$0 describe the constraintsfor manufacturing both packs.
6 Use the profit function f(x) 550x180yand theconstraints given to determine the maximum profit for manufacturing both backpacksfor the given constraints.$620xyOxyOxyOxyOxyOxyOKuta Software - Infinite Algebra 2 Name_____ Period____Date_____Points in Three DimensionsDescribe the location of each point in relation to the ) (2, 4, 3)2) (0, 2, 4)3) (1, 1, 2)4) ( 1, 4, 1)5) ( 2, 4, 4)6) (1, 1, 1)Write the coordinates of each ) zyx8) zyx9) zyx10) zyx11) zyx12) zyx-1-Plot each ) (3, 1, 1)zyx14) ( 3, 4, 0)zyx15) (3, 4, 2)zyx16) (1, 4, 4)zyx17) ( 4, 4, 4)zyx18) (3, 4, 1)
7 Zyx-2-Kuta Software - Infinite Algebra 2 Name_____ Period____Date_____Solving Systems of Three Equations w/ SubstitutionSolve each system by ) x = 4 y 11 3 x + 4 z = 7 y = 5 x + 2 z + 252) x = 4 y + 4 z + 4 z = 5 x 25 2 x 5 z = 173) z = 4 x + 4 y + 13 x + 2 y 2 z = 10 x = 2 z + 104) z = 2 x + 5 y + 24 x = 3 y 3 z + 21 5 y 3 z = 245) 5 x 3 y + z = 4 2 x 2 y + 2 z = 4 z = x + 56) 4 x + 2 z = 14 y = x + z + 12 2 x 4 z = 22-1-7) 3 x 3 y = 6 z = 3 x 3 y + 9 4 x + 5 y + z = 88) x = 5 y + 4 z + 1 x 2 y + 3 z = 1 2 x + 3 y z = 29) 2 r 2 s + 2 t = 4 4 r + 2 t = 16 r + s + 6 t = 1210) 6 x + y 4 z = 3 5 x 3 y = 8 x 5 y = 411) 4 y + 5 z = 19 5 x 5 y 6 z = 8 2 x + z = 512)
8 4 r + 2 s = 12 4 r 4 s 2 t = 4 4 r + 3 t = 10-2-Kuta Software - Infinite Algebra 2 Name_____ Period____Date_____Solving Systems of Three Equations w/ EliminationSolve each system by ) x 5 y 5 z = 2 4 x 5 y + 4 z = 19 x + 5 y z = 202) 4 x 5 y z = 18 2 x 5 y 2 z = 12 2 x + 5 y + 2 z = 43) x 5 y + z = 17 5 x 5 y + 5 z = 5 2 x + 5 y 3 z = 104) 4 x + 4 y + z = 24 2 x 4 y + z = 0 5 x 4 y 5 z = 125) 4 x y + 6 z = 27 4 x 2 y + 3 z = 21 4 x 6 y + 2 z = 126) 5 a b 3 c = 17 2 a b + 6 c = 1 6 a b + 3 c = 14-1-7) 3 x 6 y + 5 z = 2 3 x + 3 y z = 5 5 x + 6 y + 5 z = 68) 4 x 2 y + z = 19 6 x + 2 y 6 z = 8 4 x + 2 y 5 z = 69) 6 x 6 y 4 z = 10 5 x + 4 y z = 12 2 x + 3 y 2 z = 910)
9 3 r + 2 s + 3 t = 23 r 4 s + 4 t = 21 3 r + s t = 1911) x + 2 z = 9 x 3 y 4 z = 2 3 x 2 y + 2 z = 1712) 2 y + 2 z = 6 6 x + 5 y + 2 z = 12 4 x y z = 1 Critical thinking question:13) Write a system of equations with thesolution (2, 1, 0).-2.
