In Exercises 1-4, write the simplex tableau for the given linear pro-gramming problem. You do not need to solve the problem. (In eachcase the objective function is to be maximized.)4. Objective function:z = 6x₁ - 9x2Constraints:2x₁ - 3x₂ ≤ 6+x₂ = 20X1, X₂0X1

Linear programming is a mathematical technique that is also used in operations management…

Answered: In Exercises 1-4, write the simplex…

Practical Management Science

6th Edition

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Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

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

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Consider the given LP:Maximize z = 4x1 + 6x2 + 8x3Subject to 3x1 + 2x2 + 5x3<= 30 9x1 + 2x2 + 7x3 <= 126 2x1 + 3x2 + x3<= 60 xi>= 01-Find the optimal values of Z, x1, x2, x3 by using the simplex method.3-If the RHS of the constraint 1 is 34 instead of 30, what is the new value of Z?
Based on Morrison and Wheat (1984). When his team is behind late in the game, a hockey coach usually waits until there is one minute left before pulling the goalie out of the game. Using simulation, it is possible to show that coaches should pull their goalies much sooner. Suppose that if both teams are at full strength, each team scores an average of 0.05 goal per minute. Also, suppose that if you pull your goalie you score an average of 0.08 goal per minute and your opponent scores an average of 0.12 goal per minute. Suppose you are one goal behind with five minutes left in the game. Consider the following two strategies: ■ Pull your goalie if you are behind at any point in the last five minutes of the game; put him back in if you tie the score. ■ Pull your goalie if you are behind at any point in the last minute of the game; put him back in if you tie the score. Which strategy maximizes your probability of winning or tying the game? Simulate the game using 10-second increments of…
a. Identify the feasible solution. b. Obtain the optimal solution. Note: Assumer or determine the objective function from available data.
MacBurger has just opened a fast-food restaurant inBloomington. Currently, i0 customers frequent MacBurger(we call these loyal customers), and N i0 customers frequentother fast-food establishments (we call these nonloyalcustomers). At the beginning of each month, MacBurger mustdecide how much money to spend on advertising. At the endof a month in which MacBurger spends d dollars onadvertising, a fraction p(d) of the loyal customers becomenonloyal customers, and a fraction q(d) of the nonloyalcustomers become loyal customers. During the next 12months, MacBurger wants to spend D dollars on advertising.Develop a dynamic programming recursion that will enableMacBurger to maximize the number of loyal customers thecompany will have at the end of month 12. (Ignore thepossibility of a fractional number of loyal customers.)
Estimate a range for the optimal objective value for the following LPs: *(a) Minimize z = 5x₁ + 2x₂ subject to (b) Maximize z subject to x₁ + 5x₂ + 3x3 X₁ X₂ ≥ 3 2x₁ + 3x₂ = 5 X1, X₂ ≥ 0 x₁ + 2x₂ + x3 = 30 2x₁ - x₂ = 40 X1, X2, X3 ≥ 0
FIND THE OPTIMUM SOLUTION TO X= Y= MAX Z=
4. Consider the following linear programming problem: Maximize Z=$15x + $5y, subject to (1) 2x + y ≤ 10 and (2) 4x + 3y ≤ 24 and (3) x, y ≥ 0. Will the optimal solution change if the objective function becomes Maximize Z=$15x + $20y (constraints remain the same)? Select one: a. Can't determine given the information. b. Yes, it will change. c. No, it remains the same.
A matrix is said to be upper triangular if for i > j, aij=0. Show that the determinant of any upper triangular 3* 3matrix is equal to the product of the matrix’s diagonalelements. (This result is true for any upper triangular matrix.)
Use the simplex iteration method each of the objective function using the same constrains Maximize Z=3X1-X2+3X3+4X4 Minimize Z=5x1-4x2+6x3-8x4 Constrains x1+2x2+2x3+4x4=<40 2x1-x2+x3+2x4=<8 4x1-2x2+x3-x4=<10 x1, x2, x3, x4=>0
You have prepared a coin flipping simulation. In your simulation, a value of less than 0.5 is designated as "Heads". Your simulation generates the following random numbers: 0.702, 0.345, 0.815, 0.047, 0.195, 0.783, 0.152, 0.698, 0.365, 0.997. (Do not round intermediate calculations.) How many trials ended in the result "Heads"? Heads How many trials ended in the result "Tails"? Tails LO

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In Exercises 1-4, write the simplex tableau for the given linear pro- gramming problem. You do not need to solve the problem. (In each case the objective function is to be maximized.)