Set up Exercises 27–31 for solution by the simplex method. First express the linear constraints and objective function, then add slack variables to convert each constraint into a linear equation, and then set up the initial simplex tableau. The solutions of some of these problems will be completed in the exercises for the next section.
Manufacturing Bicycles A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both aluminum and steel. The company has available 91,800 units of steel and 42,000 units of aluminum. The racing, touring, and mountain models need 17, 27, and 34 units of steel, and 12, 21, and 15 units of aluminum, respectively. How many of each type of bicycle should be made in order to maximize profit if the company makes $8 per racing bike, $12 per touring bike, and $22 per mountain bike? What is the maximum possible profit?
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Finite Mathematics (11th Edition)
Additional Math Textbook Solutions
Excursions in Modern Mathematics (9th Edition)
Mathematics All Around (6th Edition)
Finite Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
A Survey of Mathematics with Applications (10th Edition) - Standalone book
Mathematics for the Trades: A Guided Approach (10th Edition) - Standalone book
- Formulate and solve a linear programming model to assist the park’s management to plan and schedule the number of new employees it hires each week in order to minimize the total number of new employees it must hire during the summer.arrow_forwardProduct Blend Example Petroleum Mix Inputs Component 1 2 3 Petroleum Mix Products Component Specifications Grade Super Premium Maximum Barrels Available/Day 4,500 2,700 3,500 Extra At least 50% of 1 Not more than 30% of 2 At least 40% of 1 Not more than 25% of 3 At least 60% of 1 At least 10% of 2 Cost/Barrel $12 10 14 Selling Price/Barrel $23 20 18 • Produce at least 3,000 Barrels of each grade.arrow_forwardDetermine 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, X₂20arrow_forward
- Just make the linear programming model of the next exercise: A person wins 10 million dollars in a lottery and is advised to invest in two types of shares, A and B. Type A has more risk but produces a benefit of 10%. Those of type B are safer, but produce only 7% per year. After several deliberations, he decides to invest a maximum of 6 million in the purchase of A shares and, at least, 2 million in the purchase of B shares. Furthermore, he decides that the amount invested in A is at least equal to the amount invested in B. How should you invest 10 million so that the annual benefit is maximum? Please be as clear as possible showing all the stepsarrow_forwardWrite the transportation problem as a linear programming problem in terms and solvent of x and y and solve. (Indicate the number of units that should be transported from each factory to each depot and the total transportation cost.)arrow_forwardWrite a resource constraint for this situation: A lawn service company has 40 hours of worker time available. Mowing a lawn (x) takes three hours and trimming (y) takes two hours. The profit from mowing is $15 and the profit from trimming is $10.arrow_forward
- esc The head coach Adelaide University Judo Club has designed two training programs to prepare their judokas for the upcoming regional championship taking place in 8 weeks. Program A focuses on developing power and speed, while program B emphasises endurance and agility. Program A consists of 50 minutes of endurance, 40 minutes of agility and 30 minutes of strength training. On the other hand, program B provides 50 minutes of endurance, 25 minutes of agility and 40 minutes of strength training. Page 5 of 5 Program A costs $75 a session and program B costs $125 per session. Throughout the 8-week training period, the Judo coaches will closely monitor each player's progress, adjust their training program as needed, and provide additional support and guidance to ensure that they are fully prepared for the regional championship. The aim of the program is to enhance athlete performance by maximising their training across the 3 areas of endurance, agility, and strength. Each Judoka requires…arrow_forwardThe picture attached represents the traffic entering and leaving a "roundabout" road junction. Such junctions are very common in Europe. Construct a system of equations that describes the flow of traffic along the various branches. What is the minimum flow possible along the branch BC? What are the other flows at that time? (units are vehicles per hour.)arrow_forwardA publishing company sells 625,000 copies of certain books each year. It costs the company $1 to store each book for a year. Each time it must print additional copies, it costs the company $500 to set up the presses. How many books should the company produce during each printing in order to minimize its total storage and setup costs? The company should produce books each printing in order to minimize costs.arrow_forward
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell