3. Consider the following dual problemMinimize Z = 7x₁ + 2x₂ + 5x3 + 4x4subject to 2x₁ + 4x₂ + 7x3 + x4 ≥ 58x₁ + 4x2 + 6x3 + 4x4 ≥ 83x₁ + 8x₂ + x3 + 4x4 ≥ 4and x₁ ≥ 0, x₂ ≥ 0, X3 ≥ 0, X4 ≥ 0.(a) Construct the primal problem corresponding to this problem.(b) Solve the primal problem by the original simplex method (in tabular form) step by step.Identify the complementary basic solution for the dual problem obtained at each iteration.Use the dual simplex method manually to solve the dual problem. Compare the resultingsequence of basic solutions with the complementary basic solutions obtained in part (b).(c)

Given, a dual linear programming problem.The objective is to minimize the expression Subject to the…

Answered: 3. Consider the following dual problem…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 37CR

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4. Maximize Z = $140x₁ + $150x₂ subject to: 8x1 + 2x2 40 9x2 + 3x2 ≤ 120 X1, X₂ ≥ 0
A trailer manufactor has multiple products designed to be towed by a pickup (Ford F-150, Toyota Tacoma, etc). The production of one of their products - the XL7 5x10 trailer - referred to as XL7510 here, has a fixed 9 cost of $62,175 and a variable cost per unit of XL7510 equal to 181 + - dollars, where x is the total 10 number of XL7510s produced. Suppose further that the selling price of this product is 1085 The -values of the break-even points are The maximum revenue is Form the profit function: P(x) The maximum profit is = The price that will maximize profit is 1 - dollars per unit of XL7510. 10 dollars (round to the nearest cent) dollars (round to the nearest cent)
A trailer manufactor has multiple products designed to be towed by a pickup (Ford F-150, Toyota Tacoma, etc). The production of one of their products - the XL7 5x10 trailer - referred to as XL7510 here, has a fixed 7 cost of $56,048 and a variable cost per unit of XL7510 equal to 214 + - dollars, where is the total number of XL7510s produced. 10 Suppose further that the selling price of this product is 1180 The -values of the break-even points are The maximum revenue is Form the profit function: P(x) = The maximum profit is The price that will maximize profit is 3 10 - dollars per unit of XL7510. dollars (round to the nearest cent) dollars (round to the nearest cent)
4. Maximize Z = 3x1 + 2x2 + x3 5. Maximize Z = 2x1 + x2 – 2x3 Subject to 2xı +x2 + x3 < 150 2х, + 2х, + 8х3 < 200 2х, + 3x, + хз < 320 X1 , X2, X3 2 0 Subject to -2x1 + x2 + x3 2 -2 - x1 + x2 – x3 2 -4 X1 + x2 + 2x3 <6 X1 ,X2,X3 2 0
maximize 2x₁ + x₂ - 3 subject to 4x₁ + x₂ + 3x3 ≤ 1, -2x2 + x3 ≤ ₁, 4x2 + 2x3 = -7, ₁ ₂ ≤ 0, unrestricted, T3 20
A trailer manufactor has multiple products designed to be towed by a pickup (Ford F-150, Toyota Tacoma, etc). The production of one of their products - the XL7 5x10 trailer - referred to as XL7510 here, has a fixed 1 cost of $66,240 and a variable cost per unit of XL7510 equal to 202 + dollars, where it is the total number of XL7510s produced. I I Suppose further that the selling price of this product is 1194 The x-values of the break-even points are The maximum revenue is Form the profit function: P(x) = The maximum profit is The price that will maximize profit is dollars per unit of XL7510. dollars (round to the nearest cent) dollars (round to the nearest cent)
B. Convert primal problem to dual problem: Minimize Z = 4x₁ + 2x₂-x3 Subject to: x₁ + x₂ + 2x3 23 2x₁2x2 + 4x3 ≤ 5 X1, X2, X3 20
2. Minimize z - 6х, + 6х, + 8x, + 9х, subject to X, + 2xz + x3+ X4 2 3 2x, + xz + 4x3 + 9x42 8 X, 2 0, x2 2 0, x3 2 0, x,2 0.
B. Convert primal problem to dual problem: Minimize Z = 4x₁ + 2x₂ = x3 Subject to: x₁ + x₂ + 2x3 ≥ 3 2x₁2x₂ + 4x3 ≤ 5 X1, X2, X3 20
1. Ten year old Kayla's lemonade stand has experienced rises and falls in sales caused by temperature changes over the last few weeks. Her sales over the first few weeks of the summer were stacked according to the model S(x) =2x³ – 32x2 + 128x + 6 , where x is the number of weeks and S(x) is the number of sales. a) Kayla makes a profit if she sells at least 6 glasses of lemonade. Use the model to determine the number of days that she made a profit. b) What are the domain and range? Interpret each. c) Predict the number of sales on her last week of sales (Assume 12 weeks). Does this seem reasonable? What kind of conclusions would you make about the weather with this model?

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