1. Consider the following constrained optimization problem: you have to decide about purchasing , and x2...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. Consider the following constrained optimization problem: you have to decide about purchasing ₁, and x2 units of goods with prices p₁, p2 (per unit). Utility of these goods in the production (output) is described by the utility function: 1-a u(x₁, x₂) = axix 1/2 - where a € (0, 1) and a > 0 is a given constant. 2 You are given the fixed utility U that must be achieved by the purchased amounts (i.e. u(x₁, x₂) = U) while the total cost p₁x₁ + p2x2 is minimized. a) Formulate the optimization problem to be solved. [2] b) Find the solution of the problem. [5] c) How will the optimal cost of the purchase change if the total utility U is de- creased by 2%. [3] 1. Consider the following constrained optimization problem: you have to decide about purchasing ₁, and x2 units of goods with prices p₁, p2 (per unit). Utility of these goods in the production (output) is described by the utility function: 1-a u(x₁, x₂) = axix 1/2 - where a € (0, 1) and a > 0 is a given constant. 2 You are given the fixed utility U that must be achieved by the purchased amounts (i.e. u(x₁, x₂) = U) while the total cost p₁x₁ + p2x2 is minimized. a) Formulate the optimization problem to be solved. [2] b) Find the solution of the problem. [5] c) How will the optimal cost of the purchase change if the total utility U is de- creased by 2%. [3]
Expert Answer:
Related Book For
Introduction to Operations Research
ISBN: 978-1259162985
10th edition
Authors: Frederick S. Hillier, Gerald J. Lieberman
Posted Date:
Students also viewed these mathematics questions
-
Jacobs asked Dean to present her findings to the larger community of employees at the firm. Several representatives of the manufacturing departments were present, as well as the general sales...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
Consider the following constrained optimization problem: Maximize f(x) = 6x + 3x2 2x3, Subject to x 0.
-
Here are the supply and demand equations for throstles, where p is the price in dollars: D (p) = 40 p S (p) = 10+p. On the axes below, draw the demand and supply curves for throstles, using blue...
-
A force P is slowly applied to a plate that is attached to two springs and causes a deflection n x0. In each of the two cases shown, derive an expression for the constant ke, in terms of k1 and k2,...
-
Sketch a two-transistor configuration using npn and pnp BJTs that are equivalent to a single pnp BJT.
-
Round Rock Corp. borrowed \(\$ 35,000\), issued common stock of \(\$ 10,000\), and paid dividends of \(\$ 25,000\). What was Round Rock's net cash provided (used) by financing activities? a. \(S 0\)...
-
Consider the following transactions of Moore Software: Mar. 31 Recorded cash sales of $170,000, plus sales tax of 5% collected for the state of new Jersey. Apr. 6 Sent March sales tax to the state....
-
Define Procedural Fairness? When would procedural fairness arise? When would mediation be suitable? What is Proof of service? How is it used? What are the forms? How would a statute or regulation...
-
In 2023, Lisa and Fred, a married couple, have taxable income of $400,000. If they were to file separate tax returns, Lisa would have reported taxable income of $225,000 and Fred would have reported...
-
Tye-Dye Company acquired machinery on Sept 1, 2023, for $1,410,000. The machinery's estimated useful life is 5 years, and the estimated residual value is $124,000. The company estimates that the...
-
To obtain an understanding of the relevant policies and procedures of internal control, the auditor performs all of the following except a. Make inquiries. b. Inspect documents and records. c. Make...
-
A graduating senior with a major in accounting is considering the following job offers. a. From a "Big Six" CPA firm. b. From a small local CPA firm. c. From a large corporation with training to...
-
The understanding of internal control that relates to a financial statement assertion should be used to do all of the following except a. Determine inherent risk for that assertion. b. Identify types...
-
Let $S^{2}$ denote a sphere of unit radius, centered at the origin of $\mathbb{R}^{3}$. What is the group of transformations that leave it invariant? Next, let $S_{(1)}^{2}$ be a sphere of unit...
-
Which of the following internal control procedures would an entity most likely use to assist in satisfying the completeness assertion related to long-term investments? a. Senior management verifies...
-
Ex: Suppose an algorithm has a complexity function: T(n) = n*log(n) + 7*n + 3*n + 11 Q: Which asymptotic notations does T(n) belong to if g(n) = n? Q: Which asymptotic notations does T(n) belong to...
-
For the data in Exercise 17-19, use the FIFO method to summarize total costs to account for, and assign these costs to units completed and transferred out, and to units in ending work in process....
-
The Fairwinds Development Corporation is considering taking part in one or more of three different development projects A, B, and Cthat are about to be launched. Each project requires a significant...
-
Tim Madsen is the purchasing agent for Computer Center, a large discount computer store. He has recently added the hottest new computer, the Power model, to the stores stock of goods. Sales of this...
-
A certain small car-wash business is currently being analyzed to see if costs can be reduced. Customers arrive according to a Poisson process at a mean rate of 15 per hour, and only one car can be...
-
Fill in the Blank. When finite amplitudes of motion are involved, __________ analysis becomes necessary.
-
Fill in the Blank. __________ equation involves time-dependent coefficients.
-
Fill in the Blank. __________ principle is not applicable in nonlinear analysis.
Study smarter with the SolutionInn App