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).

3N + 25M + P ≤ 45

Explanation:

Let the number of Newspaper Stories taken=N

Newspaper stories take 3 hours to write.

Total Hour spent on Newspaper Stories=3N

Let the number of Magazine Articles taken =M

Magazine articles take much longer to write 25 hours per article.

Total Hour spent in Magazine Articles=25M

Let the number of Proofreading jobs taken =P

Proofreading pays for every 1 hour

Total Hour spent in Proofreading jobs=P

Since both newspaper stories and magazine articles must be completed in the week they are started.

The writer doesn't want to work more than 45 hours per week. So his total hour in a week is less than or equal to 45.

The Constraint that limits the amount of time the writer will work in a week is given as:

3N + 25M + P ≤ 45

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