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Algebra II Unit 2 Review Name ________________________________ Solve Each Inequality. Graph the solution on the number line. 1. │ 2x-2 │+ 5 < 11 2. │x+13│> 9 Solve the system of 3 variables. 3. 4a + 3b + c = -17 a – 3b + 2c = -15 11a = 2b – 3c -58 4. 8x – y + z = -3 4x + 2y -3z = 7 x – 3y + 2z = -8 Solve the situation. Correctly identify solutions. 5. A stadium has 51,000 seats. Seats sell for $25 in Section A, $20 in Section B, and $15 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,093,500 from each sold out event. How many seats does each section hold? Graph the solution set to the system of inequalities. 6. y > 4 Y < x+1 7. Y ≤ -5x -5 y≥x+5 8. X + 4y ≤ 8 y>x-9 Solve the Linear Programming problem. 9. A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. Department Fabricating Finishing Labor-Hours per Ski Trick Ski Slalom Ski 6 4 1 1 Maximum Labor-Hours Available per Day 132 30 If the profit on a trick ski is $40 and the profit on a slalom ski is $50, how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? a. Identify your variables. b. Write a system of constraints. c. Graph the restraints. d. Identify vertices of the system. e. Write a function to be maximized/minimized. f. Determine which vertex yields the maximum/minimum. g. Interpret the solution to the problem. (Should be in sentence form)