3. Formulate the following as a Linear Programming Model stating the decision variables, all the problem constraints, and the objective function. (DO NOT SOLVE) Suzie and her staff make two types of leather handbags, a deluxe handbag, and a traditional handbag. It takes 2 hours to cut the leather for a deluxe handbag and 1 hour to cut the leather for a traditional handbag. It takes 6 hours to sew the deluxe together, and 4 hours to sew the traditional. It takes 2 hours to dye and dry the deluxe, and 2 hours to dye and dry the traditional. A profit of $30 is made on each deluxe sold, and a profit of $10 is made on each traditional sold. If the staff has a maximum of 10 hours for cutting, and 36 hours for sewing, and a minimum of 4 hours for dying and drying, calculate the number of deluxe and traditional bags they should produce to maximize profit? 4. Smartphone Limited conducted a marketing survey among 380 customers to gain insight about a product. The survey revealed that 200 customers prioritized battery life above all other features, 160 customers prioritized phone size above all other features, and 40 were disinterested in either feature. i) Show the information above on a Venn Diagram, using to represent the number of customers that saw battery life and phone size equally important. ii) Find x, the number of persons who finds both features equally important. iii) What is the probability that a customer finds both features equally important? iv) What is the probability that a customer chooses a phone because of battery life? 5. a) How many different car license plates can be made using-three letters followed by four digits if: i) Letters and digits can be repeated. ii) No letter can be repeated but digits can be repeated. ii) No letter can be repeated, the last digit must be a 4, and no digit can be repeated. b) A catering service offers 7 appetizers, 9 main courses, and 8 desserts. A banquet committee selects 5 appetizers, 5 main courses, and 3 desserts. In how many ways can this be done?

3. Formulate the following as a Linear Programming Model stating the decision variables, all the problem constraints, and the objective function. (DO NOT SOLVE) Suzie and her staff make two types of leather handbags, a deluxe handbag, and a traditional handbag. It takes 2 hours to cut the leather for a deluxe handbag and 1 hour to cut the leather for a traditional handbag. It takes 6 hours to sew the deluxe together, and 4 hours to sew the traditional. It takes 2 hours to dye and dry the deluxe, and 2 hours to dye and dry the traditional. A profit of $30 is made on each deluxe sold, and a profit of $10 is made on each traditional sold. If the staff has a maximum of 10 hours for cutting, and 36 hours for sewing, and a minimum of 4 hours for dying and drying, calculate the number of deluxe and traditional bags they should produce to maximize profit? 4. Smartphone Limited conducted a marketing survey among 380 customers to gain insight about a product. The survey revealed that 200 customers prioritized battery life above all other features, 160 customers prioritized phone size above all other features, and 40 were disinterested in either feature. i) Show the information above on a Venn Diagram, using to represent the number of customers that saw battery life and phone size equally important. ii) Find x, the number of persons who finds both features equally important. iii) What is the probability that a customer finds both features equally important? iv) What is the probability that a customer chooses a phone because of battery life? 5. a) How many different car license plates can be made using-three letters followed by four digits if: i) Letters and digits can be repeated. ii) No letter can be repeated but digits can be repeated. ii) No letter can be repeated, the last digit must be a 4, and no digit can be repeated. b) A catering service offers 7 appetizers, 9 main courses, and 8 desserts. A banquet committee selects 5 appetizers, 5 main courses, and 3 desserts. In how many ways can this be done?

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 33E

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