$1\mathrm{.}6.$ A maintenance manager has four objectives to optimize to the selection his maintenance strategy. He has four objectives or criteria for selection. The objectives are cost, reliability, performance, and down time. The strategies to select from are the following four: run to failure $($RF$),$ time$-$based preventive $($TP$),$ condition based $($CB$)$ and combined time and condition based. CTBC$.$ He gathered his staff and obtained the following matrix that shows the pairwise comparisons among the objectives.

Cost Reliability Performance Down Time

Cost $11/51/71$

Reliability $1(1)/(2)5$

Performance $16$

Down time $1$

$($a$)$ Compute the weight of each objective.$[5]$

The strategies were subjected to testing and scored in each objective out $10$ as shown in the next matrix. Note that for cost and down time the less the better and for the other objectives the more the better.

RT TP CB CTBC

Cost $5976$

Reliability $5687$

Performance $6769$

Down time $8566$

$($b$)$ Compute the optimal strategy using TOPSIS and weighted score.