Question 1: Solve the following linear optimization problem using the Large M methodMax Z-x,+8x2Subject toX,+3x,562x,+x;=8X1,X,20

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Answered: Question 1: Solve the following linear…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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2) REVIEW: On quiz 6 the profit function was y= x*(660-3x)-(8000+110x). We can multiply this out as y= 660x-3x-8000-110x. Use the POWER RULE to find x (the number of TVS to sell to get the most profit.) On quiz 6 we used the calculator's maximum program; we should get the same answer here using calculus.
Solve this LP problem using simplex method. Show all your solutions/tables used. Identify the optimum values of X1, X2, S1, S2, S3, and Z. Maximize Z = 3X1 + 2X2 subject to 6X1 + 4X2 <= 24 X1 + X2 <= 5 X1 <= 3 X1, X2 >= 0
Sketch the following problem graphically: max f = x2 X2 subject to g1 = X1 – (1 – x2)³ < 0 92 = x1 2 0 Find the solution graphically. Apply the optimality conditions and monotonicity rules. Discuss. (From Kuhn & Tucker, 1951.)
In this question, you will work step-by-step through an optimization problem. Many airlines restrict the size of carry on item in terms of their combined length, width and height (L+W+H). I am due to fly on an airline that states "The sum of the length, the width and height of your item must be at most 50 inches". Suppose I want to take a box (cuboid) on my trip that will allow me to carry on as much as possible, and that I also want this box to have a square base. The questions we will answer using optimization are: What dimensions should the box have, and what would be the resulting maximum volume? If the base of the box is a square whose sides have length x, and the height of the box is h (both measured in inches), enter expressions for the volume of the box, V, and the sum of the length, width and height of the box in terms of x and h. V : Sum L+W+H : Since the sum of the length, width and height must be less than or equal to 50 inches, and it is clearly best to choose this…
A firm producing two goods "X" and "Y" has the profit function Z = 640X – 20X? + 40XY – 40Y² + 320Y – 140 (a) What are the profit-maximizing level of output for each of the two goods?

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Question 1: Solve the following linear optimization problem using the Large M method Max Z-x,+8x2 Subject to X,+3x,56 2x,+X;=8 X1,X,20