Solve the linear programming problem. Minimize 4x₁ + 5x2 subject to 2x₁-4x2 ≤ 10 2x1 + x2 > 15 and X₁ ≥ 0, X₂ ≥ 0 Select one: 15 O A. Minimum = 30 when x₁ = and x₂ = 0 O B. Minimum = 75 when x₁ = 0 and x2 = 15 O C. Minimum = 20 when x₁ = 5 and x2 = 0 O D. Minimum = 33 when x₁ = 7 and x2 = 1
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- Show that ∃x (P (x) ∧ Q(x)) is not logically equivalent to (∃x P (x)) ∧ (∃x Q(x)).Recall Pigou’s example discussed in class, where there are two roads that connect a source, s, and destination, t. The roads have different travel costs. Fraction x1 of the traffic flow on route 1, and the remainder x2 on route 2. Here consider the following scenario. • The first road has “infinite” capacity but is slow and requires 1 hour travel time, T1 = 1. • The second road always requires at least 15 mins, which then increases as a function of traffic density, T2 = 0.25 + 0.75x2. If drivers act in a “selfish” manner – the user optimal scenario – all the traffic will flow on the second path, as one is never worse off. Worst case scenario for path 2, both paths take one hour. So no one is incentivized to change their behavior. 1. Assume user optimal behavior, and calculate τ the expected travel time per car. 2. If instead we could control the flows, we could minimize the expected travel time. Using the expression in part (a), calculate the optimal allocation of flows x¯1 and ¯x2…Develop a simulated annealing procedure in either R or Python to solve the following knapsack problem: (Note, this problem can be solved to optimality using integer programming; however, the focus of this question is on developing the simulated annealing method). Maximize: 12x1 + 16x2 + 22x3 + 8x4 S.T. 4x1 + 5x2 + 7x3 + 3x4 ≤ 14 xi ~ binary for all i
- Correct answer will be upvoted else downvoted. Computer science. way from block u to obstruct v is a grouping u=x0→x1→x2→⋯→xk=v, where there is a street from block xi−1 to hinder xi for each 1≤i≤k. The length of a way is the amount of lengths over all streets in the way. Two ways x0→x1→⋯→xk and y0→y1→⋯→yl are unique, if k≠l or xi≠yi for some 0≤i≤min{k,l}. Subsequent to moving to another city, Homer just recalls the two exceptional numbers L and R yet fails to remember the numbers n and m of squares and streets, separately, and how squares are associated by streets. Be that as it may, he accepts the number of squares ought to be no bigger than 32 (in light of the fact that the city was little). As the dearest companion of Homer, if it's not too much trouble, let him know whether it is feasible to see as a (L,R)- constant city or not. Input The single line contains two integers L and R (1≤L≤R≤106). Output In case it is difficult to track down a (L,R)- consistent city…<Qs 45 > Consider the following pseudo-code: I = 0; J = 0; K = 8; while (I < K – 1) //while-1 { J = J + 1; while (J < K) //while-2 { if (x[I] < x[J]) { temp = x[I]; x[I] = x[J]; x[J] = temp; } } // end of while-2 I = I +1; } // end of while-1 The cyclomatic complexity of the above is ?Subject : calculas Show that: ¬q 1) p→¬q 2) (p∧r)∨s 3) s→(t∨u) 4) ¬t∧¬u where ¬ is denied.
- Given X = {1, 2, 5, 8, 9}, Y = {3, 4, 6, 7, 8}, Z = {1, 2, 4, 6, 8} and U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Findthe following: 1. (X -Z̅) ∪ Y2. (X̅ ∪ Z) ∩ Y3. (Y ∩̅Z) ∩ X4. (X ∩ Z) - (X ∪ Y)5. Z̅ – (Y ∩ X)The tableau is not optimal for either maximization or a minimization problem. Thus, when a nonbasic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering nonbasic variable. Basic Z 0 -5 0 4 -1 -10 0 0 598 0 3 0 -2 -3 -1 5 1 12 0 1 1 3 1 0 3 0 6 1 -1 0 0 6 -4 0 0 0 Categorize the variables as basic and nonbasic and provide the current values of all the variables. AP [8] Assuming that the problem is of the maximization type, identify the nonbasic variables that have the potential to improve the value of If each such variable enters the basic solution, determine the associated leaving…Consider the following bridge crossing problem where n people with speeds s1, ··· , sn wish to cross the bridge as quickly as possible. The rules remain: • It is nighttime and you only have one flashlight. • A maximum of two people can cross at any one time • Any party who crosses, either 1 or 2 people must have the flashlight with them. • The flashlight must be walked back and forth, it cannot be thrown, etc. • A pair must walk together at the rate of the slower person’s pace. Give an efficient algorithm to find the fastest way to get a group of people across the bridge. You must have a proof of correctness for your method.
- Use a computer to plot formula 2.22 directly, as follows. Define z = qA/q, so that (l-z) = qB/q. Then, aside from an overall constant that we'll ignore, the multiplicity function is [4z(1-z)]N, where z ranges from 0 to 1 and the factor of 4 ensures that the height of the peak is equal to 1 for any N. Plot this function for N = 1, 10, 100, 1000, and 10,000. Observe how the width of the peak decreases as N increases.Please help me with these question. SHow all you work. Thank you 1. Prove that∀k ∈ N, 1k + 2k + · · · + nk ∈ Θ(nk+1). 2. Suppose that the functions f1, f2, g1, g2 : N → R≥0 are such that f1 ∈ Θ(g1) and f2 ∈ Θ(g2).Prove that (f1 + f2) ∈ Θ(max{g1, g2}).Here (f1 + f2)(n) = f1(n) + f2(n) and max{g1, g2}(n) = max{g1(n), g2(n)}This problem exercises the basic concepts of game playing, using tic-tac-toe (noughtsand crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3 = 1 and −1 to any position with O3 = 1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval (s) = 3X2(s)+X1(s)−(3O2(s)+O1(s))."Mark on your tree the evaluations of all the positions at depth 2."