SOLUTION: please help me... You are about to take a test containing questions of Type A worth four points and type B worth 7 points. You must do at least 5 questions of type A, but time

Question 180051: please help me...

You are about to take a test containing questions of Type A worth four points and type B worth 7 points. You must do at least 5 questions of type A, but time does not permit you to do more than 10. You must do at least 3 questions of type B, but time does not permit you to do more than 10. In total, you can do no more than 18 questions. How many of each type of question must you do to maximize your score? What is the maximum score?

please help its so hard and long! thanks..
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You are about to take a test containing questions of Type A worth four points and type B worth 7 points.
You must do at least 5 questions of type A,but time does not permit you to do more than 10.
You must do at least 3 questions of type B, but time does not permit you to do more than 10.
In total, you can do no more than 18 questions.
How many of each type of question must you do to maximize your score?
What is the maximum score?
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Draw a coordinate system with "A" as the horizontal and
"B" as the vertical axis.
------------------------
Draw vertical lines at B = 3 and at B = 10
Draw horizontal lines at A = 5 and at A = 10
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Let "A" be number of A questions; Let "B" be number of B questions.
-----------
"Quantity" Inequalities:
A + B <= 18
5 <= A <= 10
3 <= B <= 10
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Draw the boundary line of A <= -B + 18
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Now find the vertex values that satisfy the A and the B conditions.
They are: (3,10),(8,10),(10,8),(10,5),(3,5)
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Find the point value associated with each vertex.
Since A questions are worth 4 pts. and B questions are worth 7 pts. you get:
(3,10) is worth 12+70 = 82
(8,10) is worth 32+70 = 102
(10,8) is worth 40+56 = 96
(10,5) is worth 40+35 = 75
(3,5) is worth 12+35 = 47
==============================
So the highest point value comes when A = 8 and B = 10 which yields 102 pts..
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Cheers,
Stan H.

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