Chapter 4 Test Review. 1. Sketch the graph of the equation 3x + 5y = Sketch the graph of the equation 4x + 3y = 24.

Transcription

1 Name Chapter 4 Test Review Per. 1. Sketch the graph of the equation 3x + 5y = Sketch the graph of the equation 4x + 3y = Sketch the graph of the inequality 2x + 4y Sketch the graph of the inequality 4x + 6y 12.

2 5. Find the point of intersection of the lines whose equations are 2x + 3y = 12 and 1x + 5y = 13. A) (2, 3) B) (3, 2) C) (6, 0) D) ( 2, 3) 6. Find the point of intersection of the lines whose equations are 4x + 2y = 12 and 3x + 9y = 39. A) (5, 4) B) (10, 1) C) (1, 4) D) (2, 2) 7. With the given constraints for the following linear programming mixture problem, graph the feasible region. 2 x + 3y 1800 x 0 y 0 8. With the given constraints for the following linear programming mixture problem, graph the feasible region. x + 6y 110 x 0 y 0

3 9. With the given constraints for the following linear programming mixture problem, graph the feasible region. x + 3y 23 3 x + 7y 50 x 2 y Find the constraint inequalities and the profit formula for this linear programming mixture problem: Toni has a small business producing dried floral wreaths and table arrangements. Each wreath takes seven hours to produce, uses 12 stems of flowers, and earns a profit of $23. Each table arrangement takes five hours to produce, uses 20 stems of flowers, and earns a profit of $26. Toni can work no more than 30 hours per week and has a steady supply of 100 stems of dried flowers per week. What should Toni's production schedule be to optimize profit? 11. Find the constraint inequalities and the profit formula for this linear programming mixture problem: the Acme Construction Company builds two types of houses. Plan A requires 200 man-hours for rough construction and 70 man-hours for finish work. Plan B requires 300 man-hours for rough construction and 50 man-hours for finish work. Acme has carpenters available to provide up to 900 hours of rough construction per month and 260 hours of finish work per month. If Acme clears $7000 profit on a Plan A house and $8000 profit on a Plan B house, how should they schedule production to maximize profit? 12. Write the constraint inequalities and the profit formula for this linear programming mixture problem: Amazin' Raisin Baking Co. makes both raisin cake and raisin pie. A batch of raisin cakes requires 5 lbs. of flour, 2 lbs. of sugar, and 1 lb. of raisins. A batch of raisin pies requires 2 lbs. of flour, 3 lbs. of sugar, and 4 lbs. of raisins. There are 165 lbs. of flour, 110 lbs. of sugar, and 120 lbs. of raisins available each week. Standing orders require at least 5 batches of raisin cakes and 8 batches of raisin pies per week. If profit on a batch of raisin cakes is $35 and profit on a batch of raisin pies is $40, how many batches of each should be made per week to maximize profit?

4 13. Solve this linear programming mixture problem: Kim and Lynn produce pottery vases and bowls. A vase requires 25 oz. of clay and 5 oz. of glaze. A bowl requires 20 oz. of clay and 10 oz. of glaze. There are 500 oz. of clay available and 160 oz. of glaze available. The profit on one vase is $5 and the profit on one bowl is $3. a. mixture chart b. constraints and profit formula c. feasible region d. answer in sentence form 14. Solve this linear programming mixture problem: A small stereo manufacturer makes a receiver and a CD player. Each receiver takes eight hours to assemble, one hour to test and ship, and earns a profit of $30. Each CD player takes fifteen hours to assemble, two hours to test and ship, and earns a profit of $50. There are 160 hours available in the assembly department and 26 hours available in the testing and shipping department. What should the production schedule be to maximize profit? a. mixture chart b. constraints and profit formula c. feasible region d. answer in sentence form

5 15. Graph the feasible region identified by the inequalities: x + y 5 x + 2y 8 x 0, y Graph the feasible region identified by the inequalities: 2x + 5y 70 5x + y 60 x 0, y Find the maximum value of P, where P = 10x + 100y subject to the constraints: x 0; y 0 ; 2x + 5y 20; 2x + y Find the maximum value of P, where P = 3x + 4y subject to the constraints: x 0; y 0 ; x + 2y 8; x + y 5

6 19a. Find the solution for the transportation problem using the Northwest Corner Rule. b. Determine the total cost of the solution. 20a. Find the solution for the transportation problem using the Northwest Corner Rule. b. Determine the total cost of the solution.