Solving Optimization Problem Homework

In summary, the conversation discusses a problem involving a man traveling on both land and water and trying to determine the minimum time he takes to reach a destination. The conversation involves labeling distances and using the Pythagorean theorem and derivatives to solve the problem. The conversation also briefly mentions the concept of area, but it is not relevant to the problem. The solution involves finding the minimum time in terms of a variable, w, and determining the value of w that minimizes the time.
  • #1
chompysj
19
0

Homework Statement



879lnva.jpg


Homework Equations



a^2 + b^2 = c^2
A= (1/2)bh

The Attempt at a Solution



1)I labeled the distance traveled on the ocean as y and the distance traveled on land as x.

2)This one's kinda hard to describe: you know how the 100 yd distance and the shoreline form a triangle? I labeled the bottom of that triangle as w.

3) Pythagorean theorem:

100^2 + w^2 = y^2
(300-w)^2 + 65^2 = x^2

Area of triangle:

(300)(65) - (1/2)(300-w)(65) = 65w + (1/2)(65)(300-w)

Also, the derivatives:

dy/dt = 70 yd/min
dx/dt = 120 yd/min

This is kind of where I'm stuck. Am I on the right track with the whole w thing? Or am I headed in a completely wrong direction? Please help!
 
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  • #2
chompysj said:

Homework Statement



879lnva.jpg


Homework Equations



a^2 + b^2 = c^2
A= (1/2)bh

The Attempt at a Solution



1)I labeled the distance traveled on the ocean as y and the distance traveled on land as x.

2)This one's kinda hard to describe: you know how the 100 yd distance and the shoreline form a triangle? I labeled the bottom of that triangle as w.
Okay, so "w" is the distance from the left at which the man lands on the shore.

3) Pythagorean theorem:

100^2 + w^2 = y^2
(300-w)^2 + 65^2 = x^2

Area of triangle:

(300)(65) - (1/2)(300-w)(65) = 65w + (1/2)(65)(300-w)
Area of triangle? What in the world does area have to do with anything?

so, the derivatives:

dy/dt = 70 yd/min
dx/dt = 120 yd/min

This is kind of where I'm stuck. Am I on the right track with the whole w thing? Or am I headed in a completely wrong direction? Please help!
"Area" has nothing to do with this problem. If he goes distance y yds at 70 yd/min, how long does it take him? If he goes distance x yds at 120 yd/min, how long does it take him? What is the total time? Now use your formula to put everything in terms of your original variable, w. For what value of w is that time a minimum?


 

What is an optimization problem in the context of homework?

An optimization problem in the context of homework refers to a mathematical or computational problem that involves finding the best solution from a set of possible options, given a specific set of constraints and objectives. In other words, it is about finding the most efficient or optimal way to solve a problem.

Why is solving optimization problem homework important?

Solving optimization problem homework is important because it helps to develop critical thinking and problem-solving skills. It also allows for the application of theoretical knowledge to real-world scenarios, preparing students for future challenges in their academic and professional careers.

What are some common methods for solving optimization problem homework?

There are several methods for solving optimization problem homework, including linear programming, dynamic programming, gradient descent, and genetic algorithms. The most appropriate method will depend on the specific problem and its constraints.

What are some common challenges when solving optimization problem homework?

Some common challenges when solving optimization problem homework include identifying the correct objective function, selecting appropriate decision variables, and dealing with complex constraints. Additionally, understanding and implementing the chosen method correctly can also be a challenge.

How can I improve my skills in solving optimization problem homework?

To improve your skills in solving optimization problem homework, it is important to practice regularly and seek help from your peers or instructors when needed. It can also be helpful to review and understand different methods for solving optimization problems and to apply them to various scenarios to gain a better understanding of their strengths and limitations.

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