Knapsack 0/1 problem:Given N items where each item has some weight and profit associated with it and also givena bag with capacity W, [i.e., the bag can hold at most W weight in it]. The task is to put theitems into the bag such that the sum of profits associated with them is the maximumpossible.Given the problem is solved using a dynamic programming approach and the matrix derivedis given below, answer the below set of questions by analyzing the DP matrix.weights = [2, 3, 4, 5], profits = [1, 2, 5, 6], Capacity W = 8Capacity23Profits weights|01251614|->5100O101 2 3 40 O0 1 10 10 1O1012 2252O155013566O1361800378710 101377118 From the Knapsack DP matrix given above,what is the maximum profit earned whentheCapacity = 6weights available = [3,4,5]863Not available in the DP matrix

In the dynamic programming (DP) table of the knapsack problem, each cell typically represents the…

Answered: From the Knapsack DP matrix given…

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Knapsack 0/1 problem: Given N items where each item has some weight and profit associated with it and also given a bag with capacity W, [i.e., the bag can hold at most W weight in it]. The task is to put the items into the bag such that the sum of profits associated with them is the maximum possible. Given the problem is solved using a dynamic programming approach and the matrix derived is given below, answer the below set of questions by analyzing the DP matrix. weights = [2, 3, 4, 5], profits = [1, 2, 5, 6], Capacity W = 8 Capacity 2 3 Profits weights|0 1 2 5 16 14 |-> 5 10 0 O 10 1 2 3 4 0 O 0 1 1 0 1 0 1 O 10 1 2 2 2 5 2 O 15 50 1 356 6 O 1 3 6 18 00378 7 10 10 1 3 7 7 1 18
Consider the following code:> x <- matrix(rnorm(n = 500), ncol = 5)> varx <- var(x)Starting with varx, use two applications of the sweep() function, one dividing each row of the matrix andthe other dividing each column, of a covariance matrix to obtain R, the correlation matrix.
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From the Knapsack DP matrix given above, what is the maximum profit earned when the Capacity = 6 weights available = [3,4,5]