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Question 162579: edy is about ti take a test that contains short-answer question worth 4 points each and word problems worth 7 points each. edy must do at least 5 short-answer questions, but time rrestricts doing more than 10. she must do at least 3 word problems, but time restricts doing more than 10. edy can do no more than 18 questions in total. how many of each type of question must edy do in order to maximize her score? what is this maximum score?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Edy is about to take a test that contains short-answer question worth 4 points
each, and word problems worth 7 points each. Edy must do at least 5 short-answer
questions, but time restricts doing more than 10. She must do at least 3 word
problems, but time restricts doing more than 10. Edy can do no more than 18
questions in total. How many of each type of question must Edy do in order to
maximize her score? What is this maximum score?
:
Let x = no. of short answer problems
Let y = no. of word problems
:
x => 5; must do at least 5
x =< 10 can do no more than 10
:
y => 3; must to at least 3
y =< 10; can do no more than 10
:
x + y =< 18; Can do no more than 18 total
:
Score = 4x + 7y
It does not say to graph. Try this. Start with min x and max y
4(5) + 7(10) = 90
:
That's 15 problems, we can do 18, therefore, add 3 more short ans problems
4(8) + 7(10) = 110 is the max score
;
That seems to satisfy all constraints.
She should do 8 short ans problems, and 10 word problems for score of 110
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