Please Solve BRIEFLY like in the exam. 3. Write the dual for each of the following primal problems:(a) Maximize z = - 5x, + 2x2subject to-xi + x2s-22x1 + 3x2 55X1, x2 20(b) Minimize z = 6x1 + 3x2subject to6x1 - 3x2 + x3 2 23x1 + 4x2 + x325X1, x2, X3 20(c) Maximize z = x1 + x2subject to2x1 + x2 = 53x1 - x2 = 6X1, X2 unrestricted

(a) Primal:Maximize z=−5x1+2x2Subject to −x1+x2≤−2 2x1+3x2≤5 x1,x2≥0Here primal have…

Answered: 3. Write the dual for each of the…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.2: Guassian Elimination And Matrix Methods

Problem 10E

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A company manufactures two types of bicycles, a racing bicycle and a mountain bicycle. The total revenue (in thousands of dollars) from x1 units of racing bicycles and x2 units of mountain bicycles is R = −6x21 − 10x22 − 2x1x2 + 32x1 + 84x2 where x1 and x2 are in thousands of units. Find x1 and x2 so as to maximize the revenue
The profit function for a set of two electronics products can be expressed by the following expression: x1- 2X1 - 3X2 + 2x% where X1 = the number of product 1 units produced and X2 = the number of product 2 units produced. At least 10 units ofX1 must be produced and at least 20 units of X2 must be produced. No more than 50 units total can be produced. What type of mathematical programming model is required for this problem? a zero-one integer programming model. O a nonlinear programming model. an integer programming model. a goal programming model. O a linear programming model.
B. Convert primal problem to dual problem: Minimize Z= 4x₁ + 2x₂ - X3 Subject to: x₁ + x₂ + 2x32 3 2x₁2x₂ + 4x3 ≤ 5 X1, X2, X3 20
A stereo manufacturer determines that in order to sell x units of a new stereo, the price per unit (in dollars) must be p(x)= 3600 – 2 -x . The manufacturer also determines that the cost of producing x stereos is given by C(x) = 5000 + 40 -x . What price per unit must be charged to maximize profit? Click here to create a new row p = $
Consider the following optimization problem: Determine three positive real numbers such that their product is 237 and such that the sum of squares of these numbers is minimum. The above problem can be solved by optimizing the following objective function: xty? + x?yt + 237 A) S(x, y) x*y? + x?yt + 2372 x2 + y? B) S(x, y) C) S(x, y) = x*y? + x?y4 + 2372 x²y? aty? + x?y* + 237 ,2,,4 D) S(x, y)
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
The photocopier owner charges 7 (cents) for the first 100 copies and 4 (cents) for each copy over 100. In addition, there is a setup fee of $ 2.5 per photocopy job. As is evident in the following equations: The revenue of stripper from selling and copying is 10.07x + 2.5 for 0 100 10.04x + 5.5 for. If it costs the owner 3 cents per copy, write Matlab that determines the maximum profit per week following the following steps: Write the getData () function that requires the user to enter sales for each day of the week. Writes the () Revenue function that accepts sales data and then returns a vector that keeps the revenues calculated for each day separately. Type main script to do the following: Call the getData () function to get store sales data from the user Call the Revenue () function to find revenue for each day of the week. Call the Profit () function to find out the profit from selling every day of the week. Calculate and print for maximum profit per week. Where profit =…
Write the dual to the following problem. Maximize z = 2x1 + x2 + 3x3 + x4
The profit function for a set of two electronics products can be expressed by the following expression: / - 2X1 - 3X2 + 2 x where X1 = the number of product 1 units produced and X2 = the number of product 2 units %3D produced. At least 10 units of X1 must be produced and at least 20 units of X2 must be produced. No more than 50 units total can be produced. What is the optimal number of X2?
For each of the following problems, perform these steps: • Write the dual problem for the problem as written. • Rewrite the problem in standard form. • Write the dual of the problem in standard form. • Explain why the two dual formulations are equivalent. Maximize z = 2x, + x2 + 3x3 + 4x4 subject to 4x1 + 2x2 + 5x3 + 5x4 < 10 4x1 + 2x2 + 5x3 + 5x4 2 5 3x, + 5x2 + 4x3 + x4 2 8 3x, + 5x, + 4x3 + x4s 15 X1 + X2 + x3 + X4 = 20 x1 2 0, x2 2 0, x3 2 0, x4 0.
A manufacturer is planning to sell a total of 300 machines to both foreign and domestic firms. The price the manufacturer can expect to receive for the machines will depend on the number of machines made available. It is estimated that if the manufacturer supplies z machines to the domestic market and y machines to the foreign market, the 2y machines will sell for 900- 6x + pesos per unit domestically, and 2400 - 5y + pesos per unit abroad. 3x 5 5 (a) Express the revenues from domestic and foreign markets as functions of a and y. Then show that the total revenue is given by R(x, y) = 900x + 2400y - 6x² - 5y² + xy. (b) Evaluate R, (100, 200) and interpret this value in the context of the problem. (c) Using Lagrange multipliers to maximize revenue, how many of the 300 machines should be sold domestically, and how many should be sold abroad? What is the maximum revenue?
When deleting a basic variable xBr from the simplex tableau, would it be possible to make xBr nonbasic by pivoting on any non-zero element in row r? What difficulties one might encounter with this approach?

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