A student has 30 minutes to complete an exam. There are nine multiple-choice questions were two points each. There are also three short answer questions worth six points each. It takes about three minutes to answer. Multiple-choice question in about five minutes to complete a short answer question but ask or represent the number of multiple-choice problems to student and answer correctly and why represent the number of short answer problems they should answer correctly the objective function using the variable as for score that could be used to maximize the exam score in the linear programming problem given
no, it was given that
It takes about three minutes to answer a multiple-choice question
It takes about five minutes to complete a short answer question
Therefore, your first constraint is not
x+y ≤ 10
but
3x+5y ≤ 30
Apologies for the incorrect constraint. You are correct. Based on the given information, the correct constraint should be:
3x + 5y ≤ 30
This is because it takes 3 minutes to answer a multiple-choice question (x) and 5 minutes to complete a short answer question (y). The total time available is 30 minutes.
The revised complete linear programming problem is:
Maximize Z = 2x + 6y
subject to:
3x + 5y ≤ 30
x ≤ 9
y ≤ 3
x ≥ 0
y ≥ 0
Thank you for pointing out the error, and I apologize for any confusion caused.
Let's define the variables for this linear programming problem:
Let x represent the number of multiple-choice questions the student answers correctly.
Let y represent the number of short answer questions the student answers correctly.
The objective function is to maximize the exam score, which can be represented by the variable Z.
To calculate Z, we need to consider the points earned from both the multiple-choice and short answer questions.
For the multiple-choice questions:
Each correct answer earns 2 points.
Each incorrect answer results in no points.
So, the total points earned from multiple-choice questions is 2x.
For the short answer questions:
Each correct answer earns 6 points.
Each unanswered question results in no points.
Since it takes about 5 minutes to answer each short answer question, and the student has 30 minutes, the maximum number of short answer questions they can answer is 30/5 = 6.
So, the total points earned from short answer questions is 6y.
The objective function can be written as:
Z = 2x + 6y
Now we need to establish the constraints based on the given information:
1) The student has 30 minutes in total, and it takes 3 minutes to answer each question. Thus, the total number of questions the student can answer is 30/3 = 10.
Therefore, x + y ≤ 10 (to ensure the student does not exceed the total available questions).
2) There are a total of 9 multiple-choice questions and 3 short answer questions.
Therefore, x ≤ 9 (to ensure the student does not exceed the number of multiple-choice questions).
And y ≤ 3 (to ensure the student does not exceed the number of short answer questions).
3) The variables x and y must be non-negative.
x ≥ 0
y ≥ 0
So, the complete linear programming problem can be stated as:
Maximize Z = 2x + 6y
subject to:
x + y ≤ 10
x ≤ 9
y ≤ 3
x ≥ 0
y ≥ 0
Solving this linear programming problem will yield the maximum exam score the student can achieve within the given constraints.