1 – The Alpha Beta Corporation makes laser and inkjet printers for personal computers. Each laser printer yields $40 in profits and each ink jet printer provides $20. Each of the printers goes through two assembly areas: Dept. A and Dept. B. The following table provides processing times per unit (in minutes) as well as total available processing times per department:
Printer
Dept. A
Dept. B
Laser
9
12
Inkjet
6
8
Total available time per day
216
384
Sales commitments require at least 5 laser printers and 10 inkjet printers to be made per day. The company is interested in determining how many of each printer to produce so as to maximize its profit. What are decision variables? What is the objective function for this problem? What are the constraints? What is the optimal production quantity for each printer? How much profit the manufacturer earns with optimal production quantities?
2 – A business major student at Albany State University must complete a total of 45 courses to graduate. The minimum number of business courses required to graduate is 23 and the minimum number of non-business courses required is 15. (The remaining are elective courses; the student can choose business or non-business courses to satisfy the 45-course requirement). The average business course requires a textbook costing $100 while an average non-business courses require a textbook costing $125. The student has only $5000 for the textbook budget. A business course requires 120 hours of study per semester and a non-business course requires 90 hours of study. The student wants to minimize the total number of study hours. What are decision variables? What is the objective function for this problem? What are the constraints? What should be the course combination the student chooses? How many study hours are required? How much money is required to purchase books?
