Internally, "egg" would have a Gross Profit of $ 1.2 (0.6 x 2) & "processing" would have $ 0.1 gross profit since processing costs zero.
As far as the company is concerned total sales would be $ 2.1 (1+1.1) & gross profit would be $ 1.3 (2.1 - 0.8)
If "processing" was a subsidiary of "egg", consolidated sales & gross profit will be the same (ie $ 2.1 & $ 1.3) since you must eliminate in full intra-group assets and liabilities, equity, income, expenses and cash flows relating to transactions between entities of the group (profits or losses resulting from intragroup transactions that are recognised in assets, such as inventory and fixed assets, are eliminated in full) as per IFRS 10.