Consider the following all-integer linear program.Max 1x₁ + 1x₂s.t.4x + 6x₂ ≤ 381x₁ + 5x₂ s 152x₁ + 1x₂ 5 17X₁ X₂20 and integer(a) Graph the constraints for this problem. Use dots to indicate all feasible integer solutions.X₂X286246(b) Solve the LP Relaxation of this problem.at (x₁, x₂)=(c) Find the optimal integer solution.at (x₁, x₂)=8X₁(2468X1ⓇX₂864228x₂X₂86-68

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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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4. Find a quadratic function f(x) = ax² + bx + c which has a vertex at (1, 1) and passes through (3, –3). (Hint: first find the standard equation of this parabola and then expand this standard equation.)
Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard model requires 5 hours to assemble and 1 hours for finishing touches. The artisan model requires 2 hours to assemble and 4 hours for finishing touches. Based on their current staffing, they can manage a maximum number of assembly hours available is 50 per day, and the maximum number of finishing hours available is 64 per day. Let x = the number of standard model bookcases produced per day and y = the number of artisan model bookcases produced per day. Write the system of inequalities that represents the maximum number of bookcases that can be produced in one day. 0 Graph the system of inequalities, remember to include x >0 and y > 0 in your graph to get full credit. You will need to include four lines. 25 24 VI
Maximize the function f(x, y) = 8xy - 3x²-3x - 4y + 10 subject to the constraint 2x + 3y = f(x, y) Find the location of the maximum and its value. Enter non-integer numerical values as decimals to at least 3 decimal places. Note: you must use a . and not, for a decimal point. The maximum is located at x = Y 4 = and
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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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