Show that the linear programming problem is unbounded. Minimize g(x, y) = x-3ygun Imaniasubject tox+y≥2x-2y ≤0y - 2x ≤1x, y ≥0is unbounded. [Hint: Graph the constraint set and show that g(x, y)→→∞ asy→∞ along the line x - 2y=0.]

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Answered: Minimize subject to g(x, y) = x-3yquino…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following integer nonlinear programming problem. Маximize Z = xx3x3, XX2X3 , subject to X1 + 2x2 + 3x3< 10 x121, x 2 1, xz 2 1, and X1, X2, X3 are integers. Use dynamic programming to solve this problem. Please show your steps (show your tables).
An investor has $621,000 to invest in bonds. Bond A yields an average of 8% and the bond B yields 7%. The investor requires that at least 5 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. This can be set up as a linear programming problem. Introduce the decision variables: x= dollars invested in bond Ay= dollars invested in bond B Compute x+y. $ . Round to the nearest cent. Investor Matt has $152,000 to invest in bonds. Bond A yields an average of 9.2% and the bond B yields 8.4%. Matt requires that at least 4 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. What is the maximum return? $ per year. Round to the nearest cent. Investor Dan has $607,000 to invest in bonds. Bond A yields an average of 8.5% and the bond B yields 8.4%. Dan requires that at least 4 times as much money be invested in bond A as in…
Formulate but do not solve the following exercise as a linear programming problem. A financier plans to invest up to $400,000 in two projects. Project A yields a return of 10% on the investment of x dollars, whereas Project B yields a return of 13% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, the financier has decided that the investment in Project B should not exceed 40% of the total investment. How much should she invest in each project to maximize the return on her investment P in dollars? MaximizeP= subject to the constraints ? amount available for investment? allocation of funds?
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Explain important characteristics of situations to which linear programming method can be successfully applied. Assume a suitable example A firm manufactures three products A, B, and Time to manufacture product A is twice that for B and thrice that for C and if the entire labour is engaged in making product A, 1,600 units of this product can be produced. These products are to be produced in the ratio 3:4:5. There is demand for at least 300, 250 and 200 units of products A, B and C and the profit earned per unit is sh. 90, sh. 40 and sh. 30 respectively. Table Raw material Requirement per unit of product (kg) Total availability (kg) A B C P 6 5 2 5,000 Q 4 7 3 6,000 Formulate the problem as a linear programming problem.

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Minimize subject to g(x, y) = x-3yquino Imenia x+y≥2 x-2y ≤0 y - 2x≤1 x, y ≥0 is unbounded. [Hint: Graph the constraint set and show that g(x, y)→→∞ as y→∞ along the line x - 2y = 0.]