Consider the following all-integer linear program.1x₁ + 1x₂4x₁ + 7x₂ ≤ 271x₁ + 6x₂ ≤ 182x₁ + 1x₂ ≤ 11X₁, X₂20 and integer(a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.X2X2864Maxs.t.2246(b) Solve the LP Relaxation of this problem.at (x₁, x₂) = |1'(c) Find the optimal integer solution.at (x₁, x₂) = |8X₁8642468X1X₂86422468X₁X286242468X1

Solve the problem by graphical method:Given constraints are:4x1+7x2≤271x1+6x2≤182x1+1x2≤11Solving:…

Answered: Consider the following all-integer…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. [A-5] A boat filled with fireworks is sailing along on a path described by the rule y = 2x - 32. At the same time, an abandoned oil tanker is drifting along on a path described by 2y + 6x-206 = 0 When the two ships collide, the explosion will be visible by every vessel within a distance of 30 km. A raft filled with kittens is floating at coordinates K (21,-4). Do the kittens see the fireworks? Oil tanker 2y + 6x 206 = 0 Explosives ship y = 2x - 32 Explosion 3(24.-14 ● Kittens on a raft (21,-4)
(2-T) ABC is a small manufacturer of two types of popular all-terrain snow skis, the J and the D models. The manufacturing process consists of two principal departments: fabrication and finishing. The fabrication department has 12 skilled workers, each of whom works 7 hours per day. The finishing department has 3 workers, who also work a 7-hour shift. Each pair of J skis require 3.5 labor hours in the fabricating department and 1 labor hour in finishing. The D model requires 4 labor hours in fabricating and 1.5 labor hours in finishing. The company operates 5 days a week. ABC makes a net profit of $50 on the J model and $65 on the D model. In anticipation of the next ski-sale season, ABC must plan its production of these two models. Because of the popularity of its products and limited production capacity, its products are in high demand, and ABC can sell all it can produce each season. The company anticipates selling at least twice as many D as J models. (Use Geogebra) Write your LP…
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.)
Max Z = 2x + 3y s.t. x + y <= 3 x + 2y <= 4 For your problem: (1) Graph the LP (2) Find the Max (3) Find the range of values for the right had side of the binding constraints that make sense, if you hold the other one still. That is, you will allow one constraint to change at a time. (4) Find the delta (how much you might change the RHS) for each of the binding constraints (5) Find the shadow price for each (6) Which constraint is better to change? Why? (7) Find the range of slopes, and the exact slopes, for the objective function which will make each corner point, and each line segment between them, optimal (8) How much can you change the coefficient of x by to get the slope of the objective function in that range or at that value?
Consider the following simplex tableau. x y z s1 s2 s3 P constant -10 0 0 -1 3 1 0 300 −6 1 0 −5 1 0 0 2,750 −7 0 1 2 8 0 0 14 9 0 0 −4 −1 0 1 540 (a) State the value of each variable. x= y= z= s1= s2= s3= P= State whether the variables are basic or non-basic. x y z s1 s2 s3 P (b) Is the given simplex tableau a final tableau?
Find the optimal solution for the following model graphically. Max Z= 5X, + 2X2 Subject to, X, + X, s 10 X, 2 5 X1, X2 20
c) A student wishes to allocate her available study time of 60 hours per week between two subjects in such a way as to maximize her grade average. She formulates two functions governing the grades of each module which can be taken as: 9₁ (t₁) = 20 + 20√₁, with t₁ > 0 and 9₂ (t₂) = -80 + 3t2, with t₂ > 80/3 maximize the grade average subject to the time constraint t₁ + t₂ = 60. You do not need to show that you have obtained a maximum.

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