A freelance writer must choose how to spend her time working on several different types of projects. Newspaper stories take 3 hours to write and pay a flat rate of $45 per story. Magazine articles take much longer to write (25 hours) but pay significantly better ($400 per article). Proofreading is often tedious, but the writer can always find proofreading jobs that pay $20 per hour. The writer wants to maximize her income but doesn't want to work more than 45 hours per week. Additionally, she dislikes proofreading so she would like to spend no more than 7 hours per week on that task. Both newspaper stories and magazine articles must be completed in the week they are started (HINT: use an integer constraint to be sure that all newspaper and magazine jobs are finished within a week). What is the optimal mix of jobs for the writer to accept each week?

N = 13, M = 0, P = 6

N = 12, M = 0, P = 7

N = 6, M = 1, P = 2

N = 5, M = 1, P = 5

N = 6, M = 1, P = 0