Maximize Z = 3x₁ + 10x₂subject toX₁ + 2x₂ ≥ 84x₁ + 5x₂ = 30<5X1and x₁ ≥ 0, x₂ ≥ 0.(a) Convert the problem to the form of : Max Z=..., subject to all functional constraints in “≤ ”.(b) Find the dual problem of this problem.

Objective Functions and Constraints: Based on the given details, the objective…

Answered: Maximize Z = 3x₁ + 10x₂ subject to x₁ +…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Referring to Exhibit 1, if the right-hand side of the Total Production Provided constraint changes to 310, then the objective function value: will decrease by 160. O will decrease by 40. O will decrease by 4 O will remain the same.
Indicate which of the following is an all-integer linear program and which is a mixed-integer linear program. Write the LP Relaxation for the problem but do not attempt to solve. (a) 70x1 + 65x2 (b) Is this linear program an all-integer linear program or a mixed-integer linear program? This is an all-integer linear program. This is a mixed-integer linear program. Max Write the LP Relaxation for the problem. s.t. (1) (2) (3) Max s.t. ---Select--- (1) 9x₁ + 4.5x₂ ≤ 400 (2) 4.5X₁ + 2x₂ ≤250 (3) x₁ + x₂ ≤ 150 X₁, X₂20 and X₂ integer Min s.t. (1) Is this linear program an all-integer linear program or a mixed-integer linear program? This is an all-integer linear program. This is a mixed-integer linear program. (2) Min s.t. Write the LP Relaxation for the problem. 7x1 + 8x2 (1) 6X₁ + 8X₂ ≥ 8 (2) 6X₁ + 10x₂ ≥ 12 X₁, X₂20 and integer ---Select---
Minimize. w = 2y1 + 4y2 Subject to: 4y1 + 2y2 2 10 4y1 + y2 > 8 2y1 + y2 > 12 У1 2 0, Y2 2 0 ***Note: Notice in the constrains, the second inequality is a multiple of the last inequality. So if we multiply last inequality by 2, I would get the same terms that exist to left hand side of inequality as in equation 2. Therefore, we have dependency. When this happens, you only need one of these as using both is redundant. Because of this, assume the second inequality in the constraints is not there and solve using first and last inequality.
b) The Scott Tractor Company ships tractor parts from Omaha to St. Louis by railroad. However, a contract limits the number of railroad cars the company can secure on each branch/arc during a week. Given these limiting conditions, the company wants to know the maximum number of railroad cars containing tractor parts that can be shipped from Omaha to St. Louis during a week. Phoenix Des Moines 3 5 6. 6. 1. Dallas 2 Omaha St. Louis 7. 3 Denver 6. ActivateW O 31°C
WK Qu. 7-11 A firm has prepared the following binary... A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital. Max 35x1 + 25x2 +15x3+ 30x4 s.t. 7x1 + 8x2 +7x3 + 13x4 ≤ 18 [Constraint 1} + x4 ≥ 2 [Constraint 2} X1 + x2 + x3 X1 + X2 ≤ 1 [Constraint 3} X1 + X3 ≥ 1 [Constraint 4) X2=X4 [Constraint 5) 1, if location j is selected xj = 0, otherwise Solve this problem to optimality and answer the following questions: a. Which of the warehouse locations will/will not be selected? Location 1 will Location 2 will Location 3 will Location 4 will be selected not be selected Net present value be selected not be selected b. What is the net present value of the optimal solution? (Round your answer to the nearest whole number.) 50 c. How much of the available capital will be spent (Hint: Constraint 1…
1. Given the LP model below. Do the following: a. Formulate the new LP model. b. Set up the initial table then identify the optimum column, pivotal row, entering variable out, going variable, Zj row entries, and Cj n-Zj row entries Maximize eamings = $0.80xX₁ + $0.40X₂ + $1.20X3 - $0.10X4 subject to X₁ + 2X₂ + X3 + 5X₁150 X₂ 4X₂ + 8X₂ = 70 6X₁ + 7X₂ + 2X3 - X₂ 120 X₁, X₂, X₁, X₁Z 0
Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.
Multiple optimal solutions exist when(choose one below) (a) the objective function's level curves are parallel to a constraint (b) for at least one objective function coefficient, the allowable increase/decrease is zero. (c) for at least one constraint, the shadow price is zero. Both (a) and (b). Both (a) and (c). Both (b) and (c). All (a), (b), (c) are true.
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a. Which of the following best describes the meaning of the equation P(25) = 200? 1. When 200 calculators are sold, the profit is $25. II. When 200 calculators are sold, the profit is increasing at a rate of $25 per additional calculator III. When 25 calculators are sold, the profit is $200. IV. When 25 calculators are sold, the profit is increasing at a rate of $200 per additional calculato
FIND THE OPTIMUM SOLUTION TO X= Y= MAX Z=
Problem 7-41 Southern Oil Company produces two grades of gasoline: regular and premium. The profit contributions are $0.30 per gallon for regular gasoline and $0.50 per gallon for premium gasoline. Each gallon of regular gasoline contains 0.3 gallons of grade A crude oil and each gallon of premium gasoline contains 0.6 gallons of grade A crude oil. For the next production period, Southern has 18,000 gallons of grade A crude oil available. The refinery used to produce the gasolines has a production capacity of 50,000 gallons for the next production period. Southern Oil's distributors have indicated that demand for the premium gasoline for the next production period will be at most 20,000 gallons. a. Formulate linear programming model that can be used to determine the number of gallons of regular gasoline and the number of gallons of premium gasoline that should be produced in order to maximize tota profit contribution. If required, round your answers to two decimal places. L Let R = P =…

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Maximize Z = 3x₁ + 10x₂ subject to x₁ + 2x₂ ≥ 8 4x₁ + 5x₂ = 30 ≤ 5 X1 and x₁ ≥ 0, x₂ ≥ 0. (a) Convert the problem to the form of: Max Z=..., subject to all functional constraints in "<". (b) Find the dual problem of this problem.