Chapter $5$ Integer Programming

course schedule for the fall semester. She is considering seven $3-$credit$-$hour courses, which are shown in the following table. Also included are the average number of hours she expects to have to devote to each course each week $($based on information from other students$)$ and her minimum expected grade in each course, based on an analysis of the grading records of the teachers in each course:

$\backslash$table$[[$Course$,$Average Hours per Week,Minimum Grade$],[$Management I,$5,$B$],[$Principles of Accounting,$10,$C$],[$Corporate Finance,$8,$C$],[$Quantitative Methods,$12,$D$],[$Marketing Management,$7,$C$],[$Java Programming,$10,$D$],[$English Literature,$8,$B$]]$

An $A$ in a course earns $4$ quality credits per hour, a B earns $3$ quality credits, a C earns $2$ quality credits, a D earns $1$ quality credit, and an F earns no quality credits per hour. Brenda wants to select a schedule that will provide at least a $2\mathrm{.}0$ grade point average. To remain a full$-$time student, which she must do to continue receiving financial'aid, she must take at least $12$ credit hours. Principles of Accounting, Corporate Finance, Quantitative Methods, and Java Programming all require a lot of computing and mathematics, and Brenda would like to take no more than two of these courses. To remain on schedule and meet prerequisites, she needs to take at least three of the following courses: Management I, Principles of Accounting, Java Programming, and English Literature. Brenda wants to develop a course schedule that will minimize the number of hours she has to work each week.

a$.$ Formulate a $0-1$ integer programming model for this problem.

b$.$ Solve this model by using the computer. Indicate how many total hours Brenda should expect to work on these courses each week and her minimum grade point average.