Business, 22.07.2019 18:00, lyndah15

The 100% rule does not imply that the optimal solution will necessarily change if the percentage exceeds 100%

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Computers and Technology, 30.06.2019 11:30, myla18jabbar

Consider the problem of making change for n cents using the fewest number of coins. assume that each coin's value is an integer. a. describe a greedy algorithm to make change consisting of quarters, dimes, nickels, and pennies. prove that your algorithm yields an optimal solution. b. suppose that the available coins are in the denominations that are powers of c, i.e., the denominations are c0, c1, , ck for some integers c > 1 and k % 1. show that the greedy algorithm always yields an optimal solution. c. give a set of coin denominations for which the greedy algorithm does not yield an optimal solution. your set should include a penny so that there is a solution for every value of n. d. give an o(nk)-time algorithm that makes change for any set of k different coin denominations, assuming that one of the coins is a penny.

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History, 02.07.2019 13:20, SKYBLUE1015

What did justice brown’s verdict in plessy v. ferguson state? it was against the law to segregate people based on race. laws permitting separation are unconstitutional. separation does not necessarily imply any inequality. desegregation was the only option to solve this court case. 3rd oiption "separation does not necessarily imply any inequality."

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Computers and Technology, 25.10.2019 04:43, sobell7725

Consider the problem of making change for n cents using the fewest number of coins. assume that each coins value is an integer. a. you have available coin denominations of 1 cent, 5 cents, 10 cents, 25 cents, as in the us coins of penny, nickel, dime, quarter. assume there is infinite availability of each of these four coin denomination types. describe a greedy algorithm to make change using the fewest number of coins. b. consider your greedy algorithm and making change for n=30 cents. show that the optimal solution for making change includes your greedy choice. to do so, assume that your greedy choice is not in the optimal solution. then use the "cut and paste" argument to show that you can replace other coins by your greedy choice, therefore finding a better solution than what was assumed to be optimal. this is in contradiction to the assumption, so your greedy choice is in the optimal solution. c. although the greedy algorithm is optimal for the us coins, it is not necessarily optimal for any set of coins. give an example of a different set of made up coin denominations with different values, for which the greedy algorithm does not yield an optimal solution. your set should include a penny so that there is a solution for every value of n. as before, assume there is infinite availability of each of the coin denomination types. show specifically a counter example in which the greedy algorithm yields a change solution that is not optimal, that is, does not include the fewest number of coins. d. name another algorithmic approach that will find an optimal solution to your example in (c).

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Mathematics, 30.10.2019 00:31, lil3114

Suppose that the objective function changes to maxz = 3x1 + (7 + ∆)x2 + 5x3. write down the new simplex tableau in which x3 and x2 are basic variables. for what range of ∆ does that tableau show an optimal solution? write down an optimal solution and a formula for the optimal value for ∆ in that range. does ∆ = 4 belong to that range? find an optimal solution and the optimal value for ∆ = 4.

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