Respuesta :
Answer:
To get the highest scores, one needs to answer 4 computational problems and 8 graphical problems.
Step-by-step explanation:
Let x be the required number of computational problems one can answer
And y be the number of graphical problems one can answer.
- One cannot answer more than 12 questions in total
x + y ≤ 12
- Computational problems take 2 mins to answer and graphical problems take 4 mins to answer and there is a maximum of 40 mins for the quiz
2x + 4y ≤ 40
- Then finally, there 6 points associated with a computational problem and 10 points associated with a graphical problem and we want to maximize the number of points obtained from the test.
P(x,y) = 6x + 10y
So, the problem looks more like a linear programming problem to maximize
P(x,y) = 6x + 10y
subject to the constraints
x + y ≤ 12
2x + 4y ≤ 40
solving the constraint equations using the maximum values of the inequalities
x + y = 12
2x + 4y = 40
From the first eqn, x = 12 - y
Substituting into the second wan
2(12 - y) + 4y = 40
24 - 2y + 4y = 40
2y = 16
y = 8
x = 12 - y = 12 - 8 = 4
So, the solution of the equation of constraints, or even the graph of both constraint equation is
x = 4, y = 8
These represents the number of computational and graphical problems to maximally satisfy the constraints and maximize the required number of points.
Hope this Helps!!!
The number of computational problems is '4' and the number of graphing problems is '8' and this can be determined by forming the inequalities.
Given :
- Computation problems are worth 6 points each and graphing problems are worth 10 points each.
- Can answer a computation problem in 2 minutes and a graphing problem in 4 minutes.
- Have 40 minutes to take the quiz. You may choose no more than 12 problems to answer.
Let the number of computational problems be 'a' and the number of graphing problems be 'b'.
It is given that you may choose no more than 12 problems to answer so, the inequality becomes:
[tex]\rm a + b \leq 12[/tex] ---- (1)
It is also given that you can answer a computation problem in 2 minutes and a graphing problem in 4 minutes. You have 40 minutes to take the quiz so the inequality that shows the situation will be:
[tex]\rm 2a + 4b \leq 40[/tex] ----- (2)
Now, it is given that Computation problems are worth 6 points each and graphing problems are worth 10 points each.
P(a,b) = 6a + 10b
Now, use constraint equations (1) and (2) using maximum values.
a = 12 - b ---- (3)
Put the value of 'a' in equation (2).
2(12 - b) + 4b = 40
24 - 2b + 4b = 40
2b = 16
b = 8
Now, put the value of 'b' in equation (3).
a = 12 - 8
a = 4
These represent the number of computational and graphical problems.
For more information, refer to the link given below:
https://brainly.com/question/20383699
