Using Proper Idiom:

1.The purchasing officer has gone in search for a substituteproduct.
2.Our office has become independent fromthe Dallas office.
3.We have been in search for a qualified supervisor since August

Using Proper Idiom:

1. The purchasing officer has gone in search of a substitute product.
To find an appropriate idiom for this sentence, we can rephrase it as "The purchasing officer is searching for a substitute product." In this case, the idiom "go in search of" means to actively look for something.

2. Our office has become independent of the Dallas office.
To rephrase this sentence with an appropriate idiom, we can say "Our office has severed ties with the Dallas office." The idiom "independent of" means not relying on or being under the control of someone or something else.

3. We have been on the lookout for a qualified supervisor since August.
To find a proper idiom for this sentence, we can say "We have been fishing for a qualified supervisor since August." Here, the idiom "on the lookout for" means actively seeking or searching for something or someone, while "fishing for" is another idiom that can be used interchangeably in this context.