Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name: ________________________ Class: ___________________ Date: __________ ID: A Algebra II Honors Test Review 3-4 to 3-6 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The maximum value of a linear objective function ____ occurs at exactly one vertex of the feasible region. a. always b. sometimes c. never 2. Which of the following points lies in the plane represented by 6x + 4y + 7z = 2? a. (–5, –8, 8) b. (8, –5, 9) c. (2, 1, –2) d. (–8, 4, –3) 3. The solution to a system of three equations in three variables is ____ one point. a. always b. sometimes c. never Short Answer Solve the system by the method of substitution. ÏÔÔ ÔÔ −x − y + 2z = −10 ÔÔÔ z = −6 4. ÔÌÔ ÔÔ ÔÔÔ −x + 2y − z = 2 Ó Use the elimination method to solve the system. ÏÔÔ ÔÔ 3x + 5y + 4z = 13 ÔÔÔ 5. ÔÌÔ 5x + 2y + 3z = −9 ÔÔ ÔÔÔ 6x + 3y + 4z = −8 Ó 1 Name: ________________________ ID: A 6. Graph the point (–2, 0, 4). 7. Describe the location of the point in coordinate space. (8, –10, –4) 8. Graph −x + 2y + 2z = 6. 9. Find the equation of each trace of 3x − 2y + 12z = 24 10. Find the values of x and y that maximize the objective function P = 2x + 3y for the graph. What is the maximum value? 2 Name: ________________________ ID: A 11. Given the system of constraints, name all vertices. Then find the maximum value of the given objective function. ÏÔ ÔÔÔ x ≥ 0 ÔÔ ÔÔÔ y ≥ 0 ÌÔÔ ÔÔ 3x + 2y ≤ 12 ÔÔÔ ÔÔÔ Óx + y ≤ 5 Maximum for P = 3x + 5y 12. Suppose you make and sell skin lotion. A quart of regular skin lotion contains 2 c oil and 1 c cocoa butter. A quart of extra-rich skin lotion contains 1 c oil and 2 c cocoa butter. You will make a profit of $10/qt on regular lotion and a profit of $8/qt on extra-rich lotion. You have 24 c oil and 18 c cocoa butter. How many quarts of each type of lotion should you make to maximize your profit? What is the maximum profit? 3 Name: ________________________ ID: A 13. A food store makes a 10-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.00 per pound, cashews cost $2.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $12.00. How much of each ingredient did the store use? 14. The sum of three numbers is -2. The sum of three times the first number, twice the second number, and the third number is 9. The difference between the second number and half the third number is 10. Find the numbers. 15. You have $36 to spend on a party. Pizzas cost $12 each, chips cost $2.25 per bag, and soda costs $2 per bottle. a. b. c. Write an equation in three variables for the number of pizzas, bags of chips, and bottles of soda you can buy. Find the intercepts of the equation. Graph the equation. 4 ID: A Algebra II Honors Test Review 3-4 to 3-6 Answer Section MULTIPLE CHOICE 1. B 2. C 3. B SHORT ANSWER 4. (0, –2, –6) 5. (–3, 6, –2) 6. 7. From the origin, move 8 units forward, 10 units left, and 4 units down. 8. 9. 3x − 2y = 24 −y + 6z = 12 x + 4z = 8 maximum value at (0, 8); 24 (0, 0), (4, 0), (2, 3), (0, 5); maximum value of 25 at (0, 5) 10 qts of regular skin lotion and 4 qts of extra-rich skin lotion will give you a maximum profit of $132. 4 lb peanuts, 2 lb cashews, 4 lb raisins 10. 11. 12. 13. 14. 3, 5, and -10 1 ID: A ESSAY 15. [4] a. 12p + 2.25c + 2s = 36 b. p = 3, c =16, s = 18 c. [3] [2] [1] only two parts correct only one part correct correct answers, but no work shown 2