To determine To calculate: The number of parents and students should attend to raise the maximum amount of money in a theatre presenting a program for students and their parents on drinking and driving. Admission is $ 2.00 for parents and $ 1.00 for students. The constraints on the theatre are that the theatre can hold no more than 150 people and every two parents must bring at least one student. Explanation Given: The admission in a theatre is $ 2.00 for parents and $ 1.00 for students. The theatre has a maximum of 150 seats and every parent must bring at least one student. Calculation: To compute the number of each type of mountain bicycles to maximize the profit, use the two steps as follows: Consider x be the number of parents and y be the number of students. So, the admission fee for parents is $ 2.00 and students is $1. Thus, the objective function based on x and y is as shown below: z = 2 x + y According to the statement the inequality representing the first constraint is: the theatre cannot hold more than 150: Hence, the inequality representing constraint is shown below: x + y ≤ 150 According to the statement the inequality representing the second constraint is: two parents should bring at least 1 student: Hence, the inequality representing constraint is shown below: x y ≤ 2 1 x ≥ 2 y x − 2 y ≥ 0 Consider the first inequality constraint x + y ≤ 150 , to solve this take it as an equality x + y = 150 and compute the solutions by substituting values and the values are as follows: x 100 150 y 50 0 Now take ( 0 , 0 ) as a test point and put it in the inequality and if the inequality holds then shade the area towards test point

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ISBN: 9781323142707

Author: Blitzer

Publisher: Pearson Custom Publishing

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Chapter 8.6, Problem 21E

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To calculate: The number of parents and students should attend to raise the maximum amount of money in a theatre presenting a program for students and their parents on drinking and driving. Admission is $2.00 for parents and $1.00 for students. The constraints on the theatre are that the theatre can hold no more than 150 people and every two parents must bring at least one student.

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Chapter 8.6, Problem 20E

Chapter 8.6, Problem 22E

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