Explanation Given: Total units of aluminium and steel available with the company are 91,800 and 42,000, respectively. The racing bikes require 17, touring bikes require 27 and mountain bikes require 34 units of steel whereas the racing bikes require 12, touring bikes require 21 and mountain bikes require 15 units of aluminium. Profits are made of $8 per racing bikes, $12 per touring bikes and $22 per mountain bikes. Calculation: Assume the number of bikes manufactured under each of the three categories be represented by x 1 , x 2 and x 3 , respectively. Construct a table in order to fetch from the given information as follows. Racing Touring Mountain Amount available Steel 17 27 34 91,800 Aluminium 12 21 15 42,000 Profit $8 $12 $22 Obtain the first constraint as 17 x 1 + 27 x 2 + 34 x 3 ≤ 91 , 800 since the racing bikes require 17, touring bikes require 27 and mountain bikes require 34 units of steel as well as total units of aluminium available with the company is 91,800. Obtain the second constraint as 12 x 1 + 21 x 2 + 15 x 3 ≤ 42 , 000 since the racing bikes require 12, touring bikes require 21 and mountain bikes require 15 units of aluminium as well as total units of steel available with the company is 42,000. Obtain the objective function which represents the maximized profits which the manufacturer enjoys as follows. z = 8 x 1 + 12 x 2 + 22 x 3 The linear programming problem can be stated as follows. Maximize z = 8 x 1 + 12 x 2 + 22 x 3 subject to 17 x 1 + 27 x 2 + 34 x 3 ≤ 91 , 800 12 x 1 + 21 x 2 + 15 x 3 ≤ 42 , 000 with x 1 ≥ 0 , x 2 ≥ 0 , x 3 ≥ 0 Add slack variables to the above constraints and obtain the linear programming problem as follows

Finite Mathematics and Calculus with Applications (10th Edition)

10th Edition

ISBN: 9780321979407

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Determine the number of slack variables and name them. Then use the slack variables to convert each constraint into a linear equation. How many and which slack variables should be assigned? OA. There are three slack variables named x₁, x₂. 51. OB. There are five slack variables named x₁, x₂, S₁, S₂. 8. OC. There are two slack variables named $₁, $₂. OD. There are three slack variables named 5₁, B₂, B3 Assume the first equation using a slack variable is 4x₁-x₂ +5₁ = 183. What is the second equation after the slack variable is introduced? A. 13x₁ +6x₂ +5=247 OB. 13x₁ +6x₂ +81 +₂=247 OC. 13x, +6x2 +52 = 247 What is the third equation after the slack variable is introduced? OA 12x₁ + x₂ +5 = 318 OB. 12x₁+x₂2*318 OC. 12x₁ + x₂ +₁ +₂=318 Maximize: z=10x₁ +3x₂ subject to: with 4x₁-x2 183 13x, +6x2 < 247 12x +%₂318 x₁20, X₂20

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Finite Mathematics and Calculus with Applications (10th Edition)

Ch. 4.1 - Prob. 1YT Ch. 4.1 - Prob. 2YT Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Convert each inequality into an equation by adding...Ch. 4.1 - For Exercises 58, (a) determine the number of...Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E

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Solution Summary: The author explains the linear programming problem that includes the objective function, linear constraints, and slack variables.

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