Graph the linear inequality. 1) x + 2y 6

Transcription

1 Assignment Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the linear inequality. 1) x + 2y 6 1) 1

2 2) x + y < -3 2) 2

3 Graph the feasible region for the system of inequalities. 3) 3x + 2y -6 3) x

4 4) 2y + x -2 4) y + 3x 9 Graph the linear inequality. 4

5 5) 3x + 4y 12 5) 5

6 6) y < x + 6 6) 6

7 Graph the feasible region for the system of inequalities. 7) 3x - 2y 6 7) x

8 A manufacturer of wooden chairs and tables must decide in advance how many of each item will be made in a given week. Use the table to find the system of inequalities that describes the manufacturer's weekly production. 8) Use x for the number of chairs and y for the number of tables made per week. The number of 8) work-hours available for construction and finishing is fixed. Hours per chair Hours per table Total hours available Construction Finishing A) x + 3 x + 2 x 27 y 20 B) x + y 36 3x x + 20 C) x + 3y 27 x + 2y 20 D) x + 3y 27 x + 2y 20 9) Use x for the number of chairs and y for the number of tables made per week. The number of 9) work-hours available for construction and finishing is fixed. Hours per chair Hours per table Total hours available Construction Finishing A) 3x + 3y 48 4x + 3y 42 B) 3x + 4y 48 3x + 3y 42 C) 4x + 3y 48 3x + 3y 42 D) 3x + 4y 48 3x + 3y 42 8

9 Graph the feasible region for the system of inequalities. 10) 2x + y 4 10) x Find the value(s) of the function, subject to the system of inequalities. 11) Find the maximum and minimum of P = 11x + 5y subject to: 11) 0 x 10, 0 y 5, 3x + 2y 6. A) 110, 15 B) 25, 15 C) 135, 15 D) 135, 110 9

10 Find the value(s) of the function on the given feasible region. 12) Find the maximum and minimum of z = 17x + 9y. 12) A) 45, 27 B) 170, 27 C) 215, 170 D) 215, 27 Use graphical methods to solve the linear programming problem. 13) Maximize z = 2x + 5y 13) subject to: 3x + 2y 6-2x + 4y 8 A) Maximum of 49 4 when x = 1 2 and y = 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 34 3 when x = 2 3 and y = 2 10

11 Find the value(s) of the function on the given feasible region. 14) Find the maximum and minimum of z = 15x - 23y. 14) A) 75, 0 B) , -138 C) -138, 0 D) 75, -138 Use graphical methods to solve the linear programming problem. 15) Minimize z = 4x + 5y 15) subject to: 2x - 4y 10 2x + y 15 A) Minimum of 33 when x = 7 and y = 1 B) Minimum of 75 when x = 0 and y = 15 C) Minimum of 20 when x = 5 and y = 0 D) Minimum of 39 when x = 1 and y = 7 Find the value(s) of the function, subject to the system of inequalities. 16) Find the maximum and minimum of P = 10x - 16y subject to: 16) 0 x 5, 0 y 8, 4x + 5y 30, and 4x + 3y 20. A) -67.5, -96 B) -96, 0 C) 50, 0 D) 50,

12 Use graphical methods to solve the linear programming problem. 17) Maximize z = 8x + 12y 17) subject to: 40x + 80y 560 6x + 8y 72 A) Maximum of 92 when x = 4 and y = 5 B) Maximum of 120 when x = 3 and y = 8 C) Maximum of 96 when x = 9 and y = 2 D) Maximum of 100 when x = 8 and y = 3 18) Maximize z = 6x + 7y 18) subject to: 2x + 3y 12 2x + y 8 A) Maximum of 32 when x = 2 and y = 3 B) Maximum of 52 when x = 4 and y = 4 C) Maximum of 32 when x = 3 and y = 2 D) Maximum of 24 when x = 4 and y = 0 Find the value(s) of the function, subject to the system of inequalities. 19) Find the minimum of P = 23x + 21y + 22 subject to: 19) x 0, y 0, x + y 1. A) 22 B) 66 C) 45 D) 43 12

13 20) Find the maximum and minimum of Z = 9x + 8y subject to: 20) 0 x 10, 0 y 5, 3x + 2y 6. A) 90, 24 B) 130, 90 C) 40, 24 D) 130, 24 Provide an appropriate response. 21) If a system of inequalities includes x 1, then the feasibility region is restricted to what? 21) A) The region left of and including x = 1 B) The region right of and including x = -1 C) The region left of and including x = -1 D) The region right of and including x = 1 The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man-hours to make one SST ring. 22) How many of each type of ring should be made daily to maximize the company's profit, if the 22) 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 TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. Provide an appropriate response. 23) The feasible region of a set of two inequalities must always be unbounded. True or false? 23) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 24) Explain why the solution to a linear programming problem always occurs at a corner point 24) of the feasible region. 25) Can there be more than one point in the feasible region where the maximum or minimum 25) occurs? Explain. 26) In an unbounded region, will there always be a solution? 26) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 27) What is the least number of inequalities needed to produce a closed region? 27) A) 4 B) 3 C) 2 D) 1 13

14 State the linear programming problem in mathematical terms, identifying the objective function and the constraints. 28) A car repair shop blends oil from two suppliers. 28) Supplier I can supply at most 41 gal with 3.6% detergent. Supplier II can supply at most 67 gal with 3.2% detergent. How much can be ordered from each to get at most 100 gal of oil with maximum detergent? A) Maximize 41x + 67y Subject to: x 41 y x y 100. C) Maximize 0.032x y Subject to: x 41 y 67 x + y 100. B) Maximize 0.036x y Subject to: 0 x 41 0 y 67 x + y 100. D) Maximize 41x + 67y Subject to: x 41 y x y 100. The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man-hours to make one SST ring. 29) How many of each type of ring should be made daily to maximize the company's profit, if the 29) profit on a VIP ring is $40 and on an SST ring is $30? A) 14 VIP and 14 SST B) 12 VIP and 12 SST C) 10 VIP and 14 SST D) 14 VIP and 10 SST State the linear programming problem in mathematical terms, identifying the objective function and the constraints. 30) A breed of cattle needs at least 10 protein and 8 fat units per day. Feed type I provides 6 protein 30) and 2 fat units at $4/bag. Feed type II provides 2 protein and 5 fat units at $2/bag. Which mixture fills the needs at minimum cost? A) Minimize 4x + 2y Subject to: 6x + 2y 8 2x + 5y 10 x,. C) Minimize 2x + 4y Subject to: 6x + 2y 10 2x + 5y 8 x,. B) Minimize 4x + 2y Subject to: 6x + 2y 10 2x + 5y 8 x,. D) Minimize 4x + 2y Subject to: 6x + 2y 8 2x + 5y 10 x,. 14