In the class, we have discussed in details $[$sic$]$ Greedy for cost minimization, i$.$e$.$ Knapsack Problem & Cost minimization $[$sic$]$ & $[$sic$]$ task cost maximization.

$3\mathrm{.}1)$ Consider such an instance as follows:

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$6$

n$=6,$

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$1$

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$2$

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$6$

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S$=\{$S

$1$

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$,$S

$2$

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$,...,$S

$6$

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$\}$ and

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$2$

k$=2.$ The

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S

i

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and

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c

i

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for

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$1$

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$2$

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$6$

i$=1,2,...,6$ the collection of subset $[$sic$]$ is

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$1$

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$2$

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$6$

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c$=\{$S

$1$

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$,$S

$2$

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$,...,$S

$6$

$$

$\}$ with

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$1$

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$\{$

$1$

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$2$

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$3$

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S

$1$

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$=\{1,2,3\},$

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$2$

$=$

$\{$

$3$

$,$

$5$

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S

$2$

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$=\{3,5\},$

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$3$

$=$

$\{$

$2$

$,$

$3$

$,$

$5$

$\}$

S

$3$

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$=\{2,3,5\},$

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$4$

$=$

$\{$

$1$

$,$

$3$

$,$

$6$

$\}$

S

$4$

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$=\{1,3,6\}$ please compute the following $[$sic$]$

$($

$1$

$)$

$(1)$ the collection of subset $[$sic$]$ out by Greed $[$sic$]$ and the corresponding coverage

$($

$2$

$)$

$(2)$ the remaining subset $[$sic$]$ after the knapsack coverage, and the sensitivity approximation ratio of Greedy on the specific instance.