A student has 30 minutes to complete an exam. There are 9 multiple-choice questions worth 2 points each. There are also 3 short answer questions worth 6 points each. It takes about 3 minutes to answer a multiple-choice question and about 5 minutes to complete a short answer question. Let x represent the # of multiple choice problems the student should answer correctly and, y represent the # of short answer problems they should answer correctly.
Question 1; State the Objective Function (using the variable S for score) that could be used to maximize the exam score in the linear programming problem given
The objective function (using the variable S for score) that could be used to maximize the exam score in the linear programming problem given is:
S = 2x + 6y
The objective function, in this case, would be to maximize the exam score (S) based on the number of multiple-choice questions (x) answered correctly and the number of short answer questions (y) answered correctly.
The objective function can be represented as follows:
Maximize S = 2x + 6y
To maximize the exam score in the linear programming problem, we can define the objective function using the variable S for the score. Now, let's break down the problem:
The student has 30 minutes to complete the exam.
There are 9 multiple-choice questions worth 2 points each.
There are 3 short answer questions worth 6 points each.
It takes about 3 minutes to answer a multiple-choice question.
It takes about 5 minutes to complete a short answer question.
First, let's calculate the time it takes to answer the multiple-choice questions. Since it takes 3 minutes to answer one multiple-choice question, the total time spent on multiple-choice questions can be calculated as 3 multiplied by the number of multiple-choice questions answered correctly, x.
The time spent on multiple-choice questions: 3x
Next, let's calculate the time it takes to complete the short answer questions. Since it takes 5 minutes to complete one short answer question, the total time spent on short answer questions can be calculated as 5 multiplied by the number of short answer questions answered correctly, y.
The time spent on short answer questions: 5y
To maximize the score, the objective function, S, can be calculated as the total points earned from multiple-choice questions plus the total points earned from short answer questions.
Objective function: S = 2x + 6y
Therefore, the objective function (using the variable S for score) that could be used to maximize the exam score in this linear programming problem is: S = 2x + 6y.