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.

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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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