Respuesta :
Answer:
9 multiple choice questions and 2 short answer questions
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Explanation:
x = number of multiple choice
y = number of short answers
The statement "It takes about 2 minutes to answer a multiple choice question and about 6 minutes to complete a short answer question" means it takes 2x+6y minutes to answer x multiple choice and y short answer questions. We want this total to be 30 minutes or less.
Therefore, [tex]2x+6y \le 30[/tex] is one constraint.
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Another constraint is that [tex]0 \le x \le 9[/tex] since the most multiple choice questions you can answer is 9.
Because there are 3 short answer questions, this means another constraint is [tex]0 \le y \le 3[/tex]
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The list of constraints is:
[tex]\begin{cases}2x+6y \le 30\\0 \le x \le 9\\0 \le y \le 3\\\end{cases}[/tex]
If you were to graph and shade these regions on the xy grid, then you should get a pentagon with the following corner points
A = (0, 0)
B = (0, 3)
C = (6, 3)
D = (9, 2)
E = (9, 0)
We'll plug the coordinates of each vertex into the objective function P(x,y) = 3x+5y which will compute the number of points total after answering x multiple choice and y short answer questions. This computes the maximum points possible.
Plug in the coordinates of point A to get P(0,0) = 0
Repeat for point B to get P(0,3) = 15
Now move onto point C to get P(6,3) = 33
Then point D is P(9,2) = 37 and point E gets us P(9,0) = 27
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Summary:
P(0,0) = 0
P(0,3) = 15
P(6,3) = 33
P(9,2) = 37
P(9,0) = 27
We see that x = 9 and y = 2 produce the largest P(x,y) value of 37
Therefore, you should answer 9 multiple choice questions and 2 short answer questions. This will yield 37 points if you were to get all of those questions correct. In other words, the most points possible are 37 when given 30 minutes.
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Side note:
If you had unlimited time, then the most points possible are 9*3+3*5 = 27+15 = 42 which is the total number of points on the exam.
Getting a 37 out of 42 is a grade of about 37/42 = 0.881 = 88.1%
