Suppose that you have a piece of land to sell and you have two buyers. If...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Suppose that you have a piece of land to sell and you have two buyers. If the first buyer receives a fraction of the piece of land, the buyer will pay you U(x) dollars. Similarly, the second buyer will pay you U2(x2) dollars for a fraction of of the land. Your goal is to sell parts of your land to the two buyers so that you maximizes the total dollars you receive. (Other than the constraint that you can only sell whatever land you own, there are no restrictions on how much land you can sell to each buyer.) (a) Formulate the problem as an optimization problem of the kind minimize f(x) subject to x by specifying f and 2. Draw a picture of the constraint set. (b) Suppose that U(x) = axi, i = 1,2, where a, and a2 are given positive con- stants such that a > 02. Find all feasible points that satisfy the first-order necessary condition, giving full justification. (c) Among those points in the answer of part b, find all that also satisfy the second-order necessary condition. Suppose that you have a piece of land to sell and you have two buyers. If the first buyer receives a fraction of the piece of land, the buyer will pay you U(x) dollars. Similarly, the second buyer will pay you U2(x2) dollars for a fraction of of the land. Your goal is to sell parts of your land to the two buyers so that you maximizes the total dollars you receive. (Other than the constraint that you can only sell whatever land you own, there are no restrictions on how much land you can sell to each buyer.) (a) Formulate the problem as an optimization problem of the kind minimize f(x) subject to x by specifying f and 2. Draw a picture of the constraint set. (b) Suppose that U(x) = axi, i = 1,2, where a, and a2 are given positive con- stants such that a > 02. Find all feasible points that satisfy the first-order necessary condition, giving full justification. (c) Among those points in the answer of part b, find all that also satisfy the second-order necessary condition.
Expert Answer:
Related Book For
International Financial Management
ISBN: 978-0078034657
6th Edition
Authors: Cheol S. Eun, Bruce G.Resnick
Posted Date:
Students also viewed these mathematics questions
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Suppose the current tax system is such that the government takes some fixed percentage t of any labor income that you make. A. Some in Congress have proposed the following alternative type of tax...
-
An ATM personal identification number (PIN) consists of four digits, each a 0, 1, 2,... 8, or 9, in succession. a. How many different possible PINs are there if there are no restrictions on the...
-
Two wheels A and B have masses m A and m B and radii of gyration about their central vertical axes of k A and k B respectively. If they are freely rotating in the same direction at A and about the...
-
The Cheadle Company purchased a fleet of 20 delivery trucks for $8,000 each on January 2, 2007. It decided to use composite depreciation on a straight-line basis, and calculated the depreciation from...
-
The K&L Designs workbook contains the Sensitivity Reports for both the original problem formulation (Example 13.19) and the alternative model (Example 13.20). Explain the differences in these reports...
-
We will see in Chapter 8 that the pressure drop in fully developed pipe flow is sometimes computed with the aid of a friction factor, defined by \[ f=\frac{\Delta p}{\frac{1}{2} ho V^{2}}...
-
Carson Corporation produces and sells three products, Alpha, Beta, and Gamma, in a local market and in a regional market. At the end of the first quarter of the current year, the following income...
-
A conducting sphere of 4.0 cm radius has a cavity of 1.0 cm radius (sharing the same center). The conducting sphere has a total charge of + 15 nC. In addition, a - 12.0 nC point charge is located at...
-
Following is the current asset section from the Ralph Lauren Corporation balance sheet: The 2018 allowance consists of $202.5 for returns and $19.7 for uncollectible accounts. The amounts tor 2017...
-
Prepare journal entries to record each of the following transactions. The company records purchases using the gross method and a perpetual inventory system. May 1 Purchased merchandise with a price...
-
A Kaplan turbine is designed to develop 8,000 \(\mathrm{kW}\) shaft power. The head available is \(12 \mathrm{~m}\). Assuming speed ratio as 2.1, flow ratio as 0.6, overall efficiency as \(80 \%\),...
-
A conical draft tube having inlet and outlet diameters \(2.5 \mathrm{~m}\) and \(3.0 \mathrm{~m}\) discharges water at the outlet with a velocity of \(5 \mathrm{~m} / \mathrm{sec}\). The total length...
-
A centrifugal pump having an internal and external diameter of impeller \(150 \mathrm{~mm}\) and \(450 \mathrm{~mm}\), respectively, is running at \(1,000 \mathrm{rpm}\). It has a constant velocity...
-
A double acting reciprocating pump has a piston of \(400 \mathrm{~mm}\) diameter and piston rod of \(40 \mathrm{~mm}\) diameter. Stroke length is \(300 \mathrm{~mm}\) and speed is \(60...
-
A single stage single acting air compressor has intake pressure 1 bar and delivery pressure 10 bar. The compression and expansion follow the law \(\mathrm{pV}^{1.3}=\) constant. The piston speed and...
-
A pharmaceutical manufacturer wants to investigate the bioactivity of a new drug. A completely randomized single factor experiment was performed with three dosage levels and the following results...
-
Determine the optimal use of Applichem's plant capacity using the Solver in Excel.
-
Suppose now that Telmex has made its shares tradable internationally via cross listing on NYSE. Again using the CAPM paradigm, estimate Telmex's equity cost of capital. Discuss the possible effects...
-
What is the difference between a buy-back transaction and a counterpurchase?
-
Explain and compare forward versus backward internalization.
-
Document the CRC card for the temptation EBT.
-
Is the temptation pattern incomplete without the use of other patterns? Explain briefly.
-
What are the classes and patterns involved in defining the stable pattern for temptation?
Study smarter with the SolutionInn App