b) Write a system of linear inequalities to model the situation and graph it.

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1 Name: Date MATH 11F CHAPTER 6 REVIEW 1 Henri coaches a women s lacrosse team of 12 players He plans to buy new practice jerseys and lacrosse sticks for the team The supplier sells practice jerseys for $55 each and lacrosse sticks for $75 each Henri can spend no more than $1700 in total He wants to know how many jerseys and sticks he should buy a) Write a linear inequality to represent the situation b) Use your inequality to model the situation graphically c) Determine a reasonable solution to meet the needs of the team, and provide your reasoning 2 Jan volunteers to fold origami frogs and swans for a display She has 8 squares of green paper for the frogs and 12 squares of white paper for the swans It takes her 4 min to fold an origami frog and 3 min to fold an origami swan There must be two swans for every frog Let f represent the number of frogs Let s represent the number of swans b) Write a system of linear inequalities to model the situation c) How would you write the objective function for time, T? 3 A football stadium has seats 70% of the seats are in the lower deck 30% of the seats are in the upper deck At least tickets are sold per game A lower deck ticket costs $100, and an upper deck ticket costs $60 Let x represent the number of lower deck tickets Let y represent the number of upper deck tickets b) Write a system of linear inequalities to model the situation and graph it c) Write the objective function and use it to determine the maximum revenue

2 4 For every bouquet that is sold at a fundraising banquet, $5 goes to charity For every ticket that is sold, $18 goes to charity The organizers goal is to raise at least $8000 The organizers need to know how many bouquets and tickets must be sold to meet their goal a) Define the variables and write a linear inequality to represent the situation b) Graph the linear inequality to help you determine whether each of the following points is in the solution set The first coordinate is the number of bouquets and the second is the number of tickets i) (200, 400) ii) (600, 300) iii) (1000, 100) 5 Baskets of fruit are being prepared to sell Each basket contains at least 8 apples and more than 4 oranges Apples cost 25 each, and oranges cost 40 each The budget allows no more than $6, in total, for the fruit in each basket Let a represent the number of apples Let r represent the number of oranges b) Write a system of linear inequalities to model the situation 6 Audrey notices the number of people and dogs in a dog park There are more people than dogs There are at least 12 dogs There are no more than 40 people and dogs, in total Let d represent the number of dogs and let p represent the number of people Write a system of linear inequalities to model the situation 7 A cafeteria offers pepperoni and vegetarian pizza slices Pepperoni slices sell for $3 and vegetarian slices sell for $250 The manager noticed that every day they sell at least three times as many pepperoni slices as vegetarian slices They always sell at least 40 slices of vegetarian pizza The total sales is never more than 250 slices b) Write a system of linear inequalities to model the situation and graph it c) Write the objective function and use it to determine the maximum and minimum profits for a month

3 MATH 11F CHAPTER 6 REVIEW Answer Section 1 ANS: a) Let x represent the number of jerseys Let y represent the number of sticks {(x, y) 55x + 75y 1700, x W, y W} b) Graph the line 55x + 75y = 1700 x-intercept: x = y-intercept: y = Since (0, 0) is in the solution set, the solution set is all points to the left of the line c) eg, Henri can buy 13 practice jerseys and 13 sticks for his team for $1690 It s reasonable to have an extra jersey and an extra stick PTS: 1 DIF: Grade 11 REF: Lesson 61 OBJ: 12 Graph the boundary line between two half planes for each inequality in a system of linear inequalities, and justify the choice of solid or dashed lines 13 Determine and explain the solution region that satisfies a linear inequality, using a test point when given a boundary line TOP: Graphing linear inequalities in two variables KEY: linear inequality solution set 2 ANS: T = 3s + 4f PTS: 1 DIF: Grade 11 REF: Lesson 64 OBJ: 11 Model a problem, using a system of linear inequalities in two variables TOP: Optimization problems I: creating the model KEY: optimization problem objective function 3 ANS: y PTS: 1 DIF: Grade 11 REF: Lesson 64 OBJ: 11 Model a problem, using a system of linear inequalities in two variables TOP: Optimization problems I: creating the model KEY: optimization problem constraint

4 4 ANS: a) Let x represent the number of bouquets sold Let y represent the number of tickets sold {(x, y) 5x + 18y 8000, x W, y W} b) Graph the line 5x + 18y = 8000 x-intercept: x =1600 y-intercept: y = The solution is all the whole number points to the right of the line or on the line i) (200, 400) is above the line so it is a solution ii) (600, 300) is above the line so it is a solution iii) (1000, 100) is below the line so it is not a solution PTS: 1 DIF: Grade 11 REF: Lesson 61 OBJ: 12 Graph the boundary line between two half planes for each inequality in a system of linear inequalities, and justify the choice of solid or dashed lines 13 Determine and explain the solution region that satisfies a linear inequality, using a test point when given a boundary line TOP: Graphing linear inequalities in two variables KEY: linear inequality solution set 5 ANS: They both must be whole numbers: x W, y W PTS: 1 DIF: Grade 11 REF: Lesson 64 OBJ: 11 Model a problem, using a system of linear inequalities in two variables TOP: Optimization problems II: exploring solutions KEY: optimization problem constraint 6 ANS: d < p PTS: 1 DIF: Grade 11 REF: Lesson 66 OBJ: 11 Model a problem, using a system of linear inequalities in two variables 16 Solve an optimization problem, using linear programming TOP: Optimization problems III: linear programming KEY: optimization problem linear programming objective function systems of linear inequalities

5 7 ANS: Maximum: $730 Minimum: $460 PTS: 1 DIF: Grade 11 REF: Lesson 66 OBJ: 16 Solve an optimization problem, using linear programming TOP: Optimization problems III: linear programming KEY: optimization problem linear programming systems of linear inequalities objective function