Question 162579
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