Consider the following all-integer linear program.1x₁ + 1x₂4x₁ + 6x₂ = 341x₁ + 7x₂ = 282x₁ + 1x₂ = 15x₁x₂20 and integer(a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.X2X₂86Maxs.t.2246(b) Solve the LP Relaxation of this problem.at (x₁, x₂) =(c) Find the optimal integer solution.] at (x₁, x₂) = ([8X1Ⓡ86O2468X1X₂8468X₂862468X₁Ⓡ

Answer : 4th graph is correct .

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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Consider the following functions. f₁(x) = x, F₂(x) = x1, f3(x) = x + 7 g(x) = c₁f₁(x) + c₂f₂(x) + C3f3(x) Solve for C₁, C₂, and c3 so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution (0, 0, 0}.) {C₁, C₂, C3} = } x Determine whether f₁, f2, f3 are linearly independent on the interval (-∞, *). linearly dependent O linearly independent
Consider the following all-integer linear program. Max 1x1 + 1x2 s.t. 4x1 + 6x2 ≤ 38 1x1 + 7x2 ≤ 21 2x1 + 1x2 ≤ 17 x1, x2 ≥ 0 and integer (b) Solve the LP Relaxation of this problem. at (x1, x2) = (c). Find the optimal integer solution. at (x1, x2) =
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A local coffee shop in its busy period gets about 10 customers per minute. A typical serverworking at the counter can help customers at a rate of 2 per minute. 4(a). What is the minimum number of servers the shop needs to have to make this astable system, i.e. rho < 1? 4(b). We will assume that the server’s rate of service stays constant. However, therate at which customers come in might fluctuate. Consider customer arrival rates rangingfrom 8 per minute to 12 per minute. Conduct a sensitivity analysis on the number ofservers the shop should have during its busy period. Range the number of servers fromyour answer in 4(a) up to 5 more (that is, if you said x in (a), let c = x, x+1,…,x+5) Create simultaneous line plots similar to what was done in the M/M/c practice for thevalues of R0. Plot the c values on the x-axis and create a separate line plot for each value oflambda(customer arrival rate). Give the appropriate titles and labels and include a legend. Make sure each graph is clear…
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