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A. Maximization Problem. Niki holds two part-time jobs, Job I and Job II. She never wants to work more than a total of 12 hours a week. She has determined that for every hour she works at Job I, she needs 2 hours of preparation time, and for every hour she works at Job II, she needs one hour of preparation time, and she cannot spend more than 16 hours for preparation. If Nikki makes P40 an hour at Job I, and P30 an hour at Job II, how many hours should she work per week at each job to maximize her income? Let x = The number of hours per week Niki will work at Job I.

A. Maximization Problem. Niki holds two part-time jobs, Job I and Job II. She never wants to work more than a total of 12 hours a week. She has determined that for every hour she works at Job I, she needs 2 hours of preparation time, and for every hour she works at Job II, she needs one hour of preparation time, and she cannot spend more than 16 hours for preparation. If Nikki makes P40 an hour at Job I, and P30 an hour at Job II, how many hours should she work per week at each job to maximize her income? Let x = The number of hours per week Niki will work at Job I.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Notes on LP problems. 1. The objective function is to be maximized OR minimized. 2. All constraints are of the form ax + by ≤ c for maximization and ax+by > c for minimization. 3. All variables are constrained to by non-negative ( x ≥ 0, y ≥ 0). A. Maximization Problem. Niki holds two part-time jobs, Job I and Job II. She never wants to work more than a total of 12 hours a week. She has determined that for every hour she works at Job I, she needs 2 hours of preparation time, and for every hour she works at Job II, she needs one hour of preparation time, and she cannot spend more than 16 hours for preparation. If Nikki makes P40 an hour at Job I, and P30 an hour at Job II, how many hours should she work per week at each job to maximize her income? Let x = The number of hours per week Niki will work at Job I.
Transcribed Image Text:Notes on LP problems. 1. The objective function is to be maximized OR minimized. 2. All constraints are of the form ax + by ≤ c for maximization and ax+by > c for minimization. 3. All variables are constrained to by non-negative ( x ≥ 0, y ≥ 0). A. Maximization Problem. Niki holds two part-time jobs, Job I and Job II. She never wants to work more than a total of 12 hours a week. She has determined that for every hour she works at Job I, she needs 2 hours of preparation time, and for every hour she works at Job II, she needs one hour of preparation time, and she cannot spend more than 16 hours for preparation. If Nikki makes P40 an hour at Job I, and P30 an hour at Job II, how many hours should she work per week at each job to maximize her income? Let x = The number of hours per week Niki will work at Job I.
Let x = The number of hours per week Niki will work at Job I. Let y = The number of hours per week Niki will work at Job II. Preparation time Working hours a week Hourly rate X 2 1 40 Y 1 1 30 total hours 16 12 A.1. Translate the above matrix into a linear programming model (LP Model). Define the objective function and the constraints (structural and non- negativity). A.2. Using DESMOS, graph the constraints and take a screenshot of the feasible region or use Snipping tool. A.3. Determine the optimal solution and the optimal value of her income. A.4. Interpret the results in A.3 to answer the question.
Transcribed Image Text:Let x = The number of hours per week Niki will work at Job I. Let y = The number of hours per week Niki will work at Job II. Preparation time Working hours a week Hourly rate X 2 1 40 Y 1 1 30 total hours 16 12 A.1. Translate the above matrix into a linear programming model (LP Model). Define the objective function and the constraints (structural and non- negativity). A.2. Using DESMOS, graph the constraints and take a screenshot of the feasible region or use Snipping tool. A.3. Determine the optimal solution and the optimal value of her income. A.4. Interpret the results in A.3 to answer the question.
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