In Exercises 1–6, determine the next pivot element for the tableau.
Maximize
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Chapter 4 Solutions
Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
- In Exercises 17–24, describe the sets of points in space whose coordinates satisfy the given inequalities or combinations of equations and inequalities.arrow_forwardA garden store prepares various grades of pine bark for mulch: nuggets (x1), mini-nuggets (x2), and chips (x3). The process requires pine bark, machine time, labor time, and storage space. The following model has been developed. Maximize 9x1 + 9x2+ 6x3 (profit) Subject to Bark 5x1 + 6x2 + 3x3 ≤ 600 pounds Machine 2x1 + 4x2 + 5x3 ≤ 600 minutes Labor 2x1 + 4x2 + 3x3 ≤ 480 hours Storage 1x1 + 1x2 + 1x3 ≤ 150 bags x1, x2, x3 ≥ 0 What is the new value of the objective function, if the profit on chips increases from $6 per bag to $7 per bag? The New Value Is=arrow_forwardA chemical manufacturing plant can produce z units of chemical Z given p units of chemicalP and r units of chemical R, where: 80p75, 5p0.25 Chemical P costs $200 a unit and chemical R costs $1,400 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $168,000. A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= unitsarrow_forward
- An experiment involving learning in animals requires placing white mice and rabbits into separate, controlled environments: environment I and environment II. The maximum amount of time available in environment I is 420 minutes, and the maximum amount of time available in environment II is 624 minutes. The white mice must spend 10 minutes in environment I and 24 minutes in environment II, and the rabbits must spend 12 minutes in environment I and 16 minutes in environment II. Find the maximum possible number of animals that can be used in the experiment and find the number of white mice and the number of rabbits that can be used. number of animalsnumber of white micenumber of rabbitsarrow_forwardconstruct the initial simplex tableau for the linear programming as follows: minimize z = 4x1 + 2x2 x1- x2 ≤ 150 -x1+ x2 ≤ 150 x1 +x2 ≥ 100 x1 +x2 ≤ 350 x1 + x2 ≥ 200 x1,x2 ≥ 0arrow_forwardFind the minimum value of x +y +z² givenx+y+z=3a.,arrow_forward
- Model File Available: Major League Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves and the Minnesota Twins are playing in the World Series and that the first two games are to be played in Atlanta, the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home field advantage, suppose the probabilities of Atlanta winning each game are as follows. Game Probability of Win 1 2 3 0.59 0.54 0.49 4 0.46 5 0.49 6 0.54 7 0.49 Construct a simulation model in which whether Atlanta wins or loses each game is a random variable. Use the model to answer the following questions. (Use at least 1,000 trials.) (a) What is the average number of games played regardless of winner? (Round your answer to one decimal place.) games (b) What is the probability that the Atlanta Braves win the World Series?…arrow_forwardQ1. Use the summation convention and free subscripts to indicate the following linear system Y1 = A11X1 +a12X2 Y2 = a21X1 + azzX2arrow_forwardwhat about the constraints equations ?arrow_forward
- Write the simplex tableau, that should be used to: Maximize P = 5x1 + 2x2 subject to x1+ 7x2 <= 54x1 + 6x2 <= 1 x1, x2 >= 0label x1, x2, s1, s2, Parrow_forwardMinimize 2x + 4y, subject to the constraint 82 – 4x – 3y = 0. The minimum value of the function is (Type an exact answer in simplified form.)arrow_forwardIn Problems 9–18, solve each linear programming problemarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage