What is Maximization: Definition and 52 Discussions

Utility maximization was first developed by utilitarian philosophers Jeremy Bentham and Josh Stewart Mill. In microeconomics, the utility maximization problem is the problem consumers face: "How should I spend my money in order to maximize my utility?" It is a type of optimal decision problem. It consists of choosing how much of each available good or service to consume, taking into account a constraint on total spending (income), the prices of the goods and their preferences.

Utility maximization is an important concept in consumer theory as it shows how consumers decide to allocate their income. Because consumers are rational, they seek to extract the most benefit for themselves. However, due to bounded rationality and other biases, consumers sometimes pick bundles that do not necessarily maximize their utility. The utility maximization bundle of the consumer is also not set and can change over time depending on their individual preferences of goods, price changes and increases or decreases in income.

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  1. L

    Lagrange multipliers understanding

    Here’s my basic understanding of Lagrange multiplier problems: A typical Lagrange multiplier problem might be to maximise f(x,y)=x^2-y^2 with the constraint that x^2+y^2=1 which is a circle of radius 1 that lie on the x-y plane. The points on the circle are the points (x,y) that satisfy the...
  2. LCSphysicist

    Question about reflectivity and maximization of energy reflected

    Imagine that we have a transmitter of microwaves that radiates a linearly polarized wave whose E field is known to be parallel to the dipole direction. We wish to reflect as much energy as possible off the surface of a pond (having an index of refraction of 9.0). Find the necessary incident...
  3. T

    Maximization of a Multivariable Function

    The beginning is straight forward and I found f=x^2-2yz, which satisfies grad(f)=F. Then I calculated W= f(x,y,z)-f(0,1,1) since it's conservative. I get stuck when trying to find the max and mins. Given grad(f)=0 at extrema, we can see (0,0,0) is a point. On the boundary, I have to...
  4. opus

    Maximize Fencing for 4 Equal Pastures - 125,000 Linear Feet

    Homework Statement A rancher has 125,000 linear feet of fencing and wants to enclose a rectangular field and then divide it into four equal pastures with three internal fences parallel to one of the rectangular sides. What are the dimensions for each of the four equal pastures that will...
  5. F

    I Expectation Maximization (EM) : find all parameters

    I am tackling a technique to determine the parameters of a Moffat Point Spread Function (PSF) defined by: ## \text {PSF} (r, c) = \bigg (1 + \dfrac {r ^ 2 + c ^ 2} {\alpha ^ 2} \bigg) ^ {- \beta} ## with the parameter "(r, c) =" line, column "(not necessarily integers). The observation of a...
  6. K

    Maximization problem — Stiffest beam that can be cut from a log

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  7. petterson

    A Maximization problem using Euler Lagrange

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  8. J

    A Maximization Problem: Double Int. w/ C not Dependent on Integrals

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  9. S

    Maximization problem with simplex method

    Homework Statement Maximize the profit function P = 3x - y - 2z subject to the following x - y - z ≤ 15 2x - y + 2z ≤ 50 2x + y + z ≤ 39 , where x ≥ 0, y ≥ 0, z ≥ 0. Homework Equations Simplex method / Simplex algorithm The Attempt at a Solution Hello to everyone who is reading this. :)...
  10. rkum99

    Maximization of motor speed/torque

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  11. F

    Projectile motion maximization

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  12. A

    Can the entropy be reduced in maximization algorithms?

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  13. T

    Optimization of windmill power with use of gears

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  14. N

    Distance formula maximization problem

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  15. F

    Why this maximization approach fails?

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  16. K

    Maximizing Angular Acceleration

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  17. T

    Maximization of an Uncertainty Product

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  18. H

    MHB Linear Programming Formulation problem faced - Maximization problem

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  19. B

    MHB Lagrangian utility maximization with a ''complex'' summation

    Hello there! It's my first time posting here, I hope you guys will be good to me :). I took a one year break to study a language abroad, and now it seems like I forgot everything math-wise. I'm preparing for a test and I'm having a really hard time doing the following problem. I need to...
  20. V

    Maximization of wave interference

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  21. L

    MHB Thank you for your understanding.

    A tree trunk is shaped like a truncated cone it has 2 m of length and diameters of their bases are 10 cm and 20 cm. Cut a square straight section so that the axis of the beam coincides with the axis of the truncated cone. find the beam volume maximum that can be drawn from this form. answer...
  22. A

    What is the value of M when |x|≤ 3 in the inequality (x^2+2x+1)/(x^2+3) ≤ M?

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  23. MarkFL

    MHB Collin's question at Yahoo Answers regarding maximization of beam strength

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  24. MarkFL

    MHB Maximizing Volume of a Cuboid - Nthabiseng P's Q&A

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  25. MarkFL

    MHB S N's question at Yahoo Answers regarding revenue maximization

    Here is the question: I have posted a link to this topic so the OP can see my work.
  26. X

    Right Triangle Maximization Problem

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  27. I

    Multi-dimensional maximization method

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  28. A

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  29. E

    MHB Linear programming maximization

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  30. M

    Multivariable calculus: Maximization of volume of box with constraint

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  31. G

    Simple maximization question very confused :s

    Hey everybody! My question is: Find the value of x that maximizes the following function and the maximum value (a is constant): f(x) = x^2 subject to 0 ≤ x ≤ a. It is supposed to be solved without calculus and I'm terrible confused! how would i go about solving this? wen i plot the curve...
  32. S

    Question about probabilistic combinatorial maximization

    Hello, I have some question about probabilistic combinatorial maximization as follows: Let X = {X_1, ..., X_n} be a set of i.i.d. positive random variables, S = {s_i} be a set of all combinations of selecting m r.v.'s from X, and Y(s_i) = the sum of r.v.'s in the combination s_i ...
  33. B

    Maximization problem of tuple set

    Given a set of vectors {v_ j } = {v_1, ... v_N} and I wish to transform each vector in the following manner v_ i ' = Sum_k=1 to N ( c_ k,i) * v_i where c_ k,i is a scalar and what we are trying to solve for. such that the sum of the distances squared between each pair of transformed vectors...
  34. M

    Algorithm to solve a maximization problem

    I have two sets of vectors: A: a1, a2, a3... an B: b1, b2, b3... bm n > m and n/m is an integer, p. Each vector bi has ranked, in order of preference, a set of vectors from A. For example, b1 may "prefer" a1, a9, and a10. The only constraint on this set is that each vector ai from A appears...
  35. L

    How to Maximize Profit for Book Publisher?

    1. A publisher wants to dispose books. For 400 copies or less the price is $30 per book. For orders of more than 400 the price of each book is dropped by 2 cents for each extra book ordered beyond 400. The cost of production is $6 for each book. Find a formula for the profit function and how...
  36. chwala

    HelpSolve Maximization Problem: 1170X1 + 1110X2

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  37. Z

    Maximize Daily Profits with Cost and Price Functions | Homework Help

    Homework Statement daily Cost function C(x) = 5x + 360 -0.001x^2, where x is the number of decks company produces each day and daily cost is in dollars. Suppose that the price that each deck is sold for varies based on the equation given by p(x) = 11.30 - 0.01x, where p is the price per deck...
  38. F

    Interesting maximization problem

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  39. I

    Utility maximization of potential disasters

    I've been doing some thinking on what resources should be allocated to stymie anthropogenic global warming. Some figures: Anywhere between 88-98% of publishing climate scientists believe in some form of AGW, based on over 6 large scale surveys. In one survey, 41% of meteorologists and...
  40. C

    General question about solving force maximization problems

    I'm doing this E&M problem for fun (I'll be taking the class this fall), but now it's just starting to get frustrating. I can't really post the problem because there is a diagram, but I'm not really looking to be given the actual solution anyway, so I'll describe it to you: Two positive...
  41. H

    Maximization with constraint

    Hi, I search for the maximum of a quadric for points on a sphere. I have an affine transform A (4x4 matrix, in homogeneous coord.) and apply it to points on (and inside) a sphere x \in S_{m,r} \Leftrightarrow (x-m)^2<=r^2 . (Although I think the extremum must be on the surface of the sphere?)...
  42. N

    Maximization of |F|^2 with Constraints on Real Inputs

    Will anyone please help me to solve the problem: F(x_1,x_2,...,x_n) is a complex valued function and each x_i are real (may be positive too) numbers. I have to find the maximum of |F| (or |F|^2) w.r.t. x_i. What are the set of constraints? I don't think it will be exactly as...
  43. M

    Maximization of the sum of mutual information terms

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  44. R

    Maximizing Profits: How Many Shares to Buy for the Best Return in 6 Months?

    Hey guys I just came across this website i think its awsome..! Hope i can contribute tooo! I had a question: If a Share costs 3 dollars, and it doubles every 3 months And nother share costs 1 dollar and doubles in One month How many shares of each would you buy with 1000...
  45. M

    Constrained Maximization

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  46. N

    WriterMaximization of Differentiable Real-Valued Function with Linear Variables

    Hi everyone, Suppose f =f(x_1, x_2,...,x_n) be a real-valued, any-time differentiable function. Let each x_i=x_i(u_1, u_2,...,u_{2^n-1}) be a linear function of reall u_i's. Let f=g(u_1, u_2,...,u_{2^n-1}). Then is it right that Max f w.r.t. x_i=Max of g w.r.t. u_i? Sorry for the...
  47. R

    Linear Programming and Maximization

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  48. O

    Maximization subject equality constraint

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  49. A

    Maximize Profit: Find Optimal Production with C(x) & R(x)

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  50. Apost8

    Maximizing Box Volume with 1200cm^2 of Material

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