MinimizeC=20x₁ + 2x2subject to4x1 + x₂ 2213x₁ + x₂ 25X₁, X₂ 20a. Form the dual problem.Maximizesubject toP=y₁ +5y₂Y₁ + y₂ ≤ 20Y₁ + y₂ ≤Y1, Y₂20

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Answered: Minimize C=20x₁ + 2x2 subject to 4x1 +…

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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The purchase price of a home y (in $1000) can be approximated based on the annual income of the buyer x1 (in $1000) and on the square footage of the home x2 (in 100 ft2) according to y = ax1 + bx2 + c. The table gives the incomes of three buyers, the square footages of the home purchased, and the corresponding purchase prices of the home. Square Footage (100 ft’) x2 Income Price ($1000) x1 ($1000) y 80 21 180 150 28 250 75 18 160 a. Use the data to write a system of linear equations to solve for a, b, and c. b. Use a graphing utility to find the reduced row-echelon form of the augmented matrix. c. Write the model y = ax1 + bx2 + c. d. Predict the purchase price for a buyer who makes $100,000 per year and wants a 2500 ft2 home.
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maximize 2x₁ + x₂ - 3 subject to 4x₁ + x₂ + 3x3 ≤ 1, -2x2 + x3 ≤ ₁, 4x2 + 2x3 = -7, ₁ ₂ ≤ 0, unrestricted, T3 20
Prime Paints manufactures two types of paints, one for interior painting and the other for exterior painting. Both types require the use of two raw materials - M1 and M2, so that the maximum daily availabilities of these materials are 24 tons and 6 tons, respectively. It is known that 1 ton of the interior type of paint requires 4 tons of M1 and 2 tons of M2. On the other hand, 1 ton of the exterior type of paint requires 6 tons of M1 and 1 ton of M2. It has been established that the daily demand for interior paint cannot exceed that for the exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. The company wants to determine the optimum product mix of interior and exterior paints to maximize the total daily profit given that the profit per ton of the interior paint is 4 thousand dollars and the profit per ton of the exterior paint is 5 thousand dollars.

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Minimize C=20x₁ + 2x2 subject to 4x1 + x₂ 221 3x₁ + x₂ 25 X₁, X₂ 20 a. Form the dual problem. Maximize subject to P=y₁ +5y₂ Y₁ + y₂ ≤ 20 Y₁ + y₂ ≤ y1, y₂ 20