Linear Equations and Inequalities Question?

You are to take a mathematics achievement test. Two days before the test you receive the following instructions concerning the point values of the two kinds of question, and how many of each you must answer.

i. There are 10 questions worth 7 points each, and 16 questions worth 5 points each.

ii. You can receive credit for a maximum of 20 questions. Any others you answer will not be scored. 

iii. To receive any credit at all, you must answer at least 5 questions.

iv. The number of 5-point questions you answer must be no more than twice the number of 7-point questions.

v. The number of 5-point questions you answer must be more than 1/2 the quantity (number of 7-point questions minus 5). 

What are the optimum numbers of 5- and 7- point questions to answer in order to maximize your score?  

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