There are four candidate materials A$,$ B$,$ C and $D$ to be selected for a new part. The part is rated according to the following five material characteristics. The weighting factors are shown in parentheses.

Resistance to shattering $(10)$

Fabricability $(5)$

Weight $(8)$

Scratch resistance $(9)$

Thermal expansion $(5)$

The properties are evaluated by a panel of technical experts, and they are expressed as percentages of maximum achievable values.

Candidate Material

Property

A

B

C

D

Resistance to

shattering

$0$

$90$

$90$

$100$

Fabricability

$50$

$30$

$10$

$100$

Weight

$45$

$90$

$45$

$100$

Scratch resistance $100,90,100,5$