For each of the following programs:(1) Sketch the feasible region of the program and the direction of the objectivefunction.(2) Use you sketch to find an optimal solution to the program. State the optimalsolution give the objective value for this solution. If an optimal solution doesnot exist, state why.(3) Transform the program into standard equation form.(4) List all basic feasible solutions of your standard equation form program. Youshould give the values for both the original decision variables and the slackvariables in each of these basic feasible solutions.(a)maximise– 2x1 + x2Xị – x2 < 1,2.x1 – x2 > 1,subject to-2.x1 + 2x2 2 4,X1, x2 > 0(b)maximise xı+ 2x2subject to-x1 + 2x2 < 6,*1 + 3x212,X1, x2 > 0

Solution a: Given that maximize -2x1+12x2subject to x1-x2≤12x1-x2≥12x1+2x2≥4x1, x2≥0 The…

Answered: For each of the following programs: (1)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.4: Linear Programming

Problem 15E

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Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.
A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three ingredients, which are available in the limited quantities shown in the table. The profit on each bag of fertilizer x is 6 and on each bag of y is 5. How many bags of each product should be produced to maximize the profit? Ingredient Number of Pounds in Fertilizer x Number of Pounds in Fertilizer y Total number of Pounds Available Nitrogen 6 10 20,000 Phosphorus 8 6 16,400 Potash 6 4 12,000
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Let's create a mathematical model for the following problem: A chemical company produces a chemical mixture for a customer in 1,000-pound batches. The mixture contains three components: mercury, zinc, and potassium. The mixture must meet specific formula specifications provided by the customer. The company wants to determine the amount of mixture that can meet all requirements and minimize the total cost. The customer provides formula specifications for each batch of the mixture as follows: The mixture must contain at least 200 pounds of mercury. The mixture must contain at least 300 pounds of zinc. The mixture must contain at least 100 pounds of potassium. The cost per pound for mercury is $4, for zinc is $8, and for potassium is $9.
Use the Simplex method to find the optimal solution to the problem below Investment: An investor has at most $35,000 to invest in government bonds,mutual funds and money market funds. The average yield for government bonds,mutual funds and money market funds, are 3%, 6% and 5% respectively. Theinvestor's policy requires that the total amount invested in mutual and money marketfunds must not exceed the amount invested in government bonds. How much shouldbe invested in each type of investment in order to maximize the return? What is themaximum return?.
1) Blade-Z manufactures roller blades. The production facility has fixed costs of $200 a day and a total production costs of $5,200 per day at an output of 100 pair of skates per day. Which of the following equations represents the daily production cost for Blade-Z based on the number of skates manufactured? Let C represent the daily production cost and x represent the number of pairs of skates manufactured. 2) Erica went shopping for new clothes for school. She bought a pair of jeans for $69.11 and several shirts for $10.06 each. If x represents the number of shirts she bought, which of the following equations should be used to find y, the total cost of Erica's shopping trip? 3) Laura retired from her job recently, and she has saved about $441, 238. 00 over the course of her career. She plans to withdraw $1,779.00 each month to pay for living expenses. After a certain amount of time, the balance in Laura's account is $400,321.00. How many months have passed since Laura retired?
Valencia Products makes automobile radar detectors and assembles two models: LaserStop and SpeedBuster. Both models use the same electronic components. After reviewing the components required and the profit for each model, the firm found the following linear optimization model for profit, where L is the number of LaserStop models produced and S is the number of SpeedBuster models produced. Implement the linear optimization model on a spreadsheet and use Solver to find an optimal solution. Interpret the optimal solution, identify the binding constraints, and verify the values of the slack variables. Maximize Profit = 124 L +137 S 17 L+12 S≤5000 5L+9S≤4500 L≥0 and S≥O (Availability of component A) (Availability of component B) Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce 0 LaserStop models and SpeedBuster models. This solution gives the maximum possible profit, which is $. (Type integers or…
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please can you help with the following question with alternative working out thanks a lot
1. Maximization Model. Answer in complete solution.

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