A method of producing one or more olefins, the method comprising: pyrolizing, in a pyrolysis unit, plastic material to form a plastic derived oil; blending the plastic derived oil with a used lubricating oil to form a blended hydrocarbon feed; separating the blended hydrocarbon feed to form a light-end stream comprising primarily C 1 to C 8 hydrocarbons and a heavy hydrocarbon feed; flowing the light-end stream to a steam cracking unit; processing the heavy hydrocarbon feed to produce a steam cracking feedstock; and cracking hydrocarbons of the steam cracking feedstock and hydrocarbons of the light-end stream to produce one or more olefins; wherein the processing of the heavy hydrocarbon feed comprises: distilling the heavy hydrocarbon feed via vacuum distillation to produce a vacuum distillation residue and a vacuum distilled hydrocarbon stream; processing the vacuum distilled hydrocarbon stream via liquid-liquid extraction to produce a poly-aromatics stream comprising primarily poly-aromatics and an intermediate stream comprising paraffinic, aromatic, and naphthenic hydrocarbons; and hydroprocessing the intermediate stream to produce the steam cracking feedstock; wherein a used lubricating oil is lubricating oil that has partially or completely lost its capability of reducing the friction, heat, and wear between mechanical components after a period of usage, and/or lubricating oil that has accumulated contaminants after a period of usage. pyrolizing, in a pyrolysis unit, plastic material to form a plastic derived oil; blending the plastic derived oil with a used lubricating oil to form a blended hydrocarbon feed; separating the blended hydrocarbon feed to form a light-end stream comprising primarily C 1 to C 8 hydrocarbons and a heavy hydrocarbon feed; flowing the light-end stream to a steam cracking unit; processing the heavy hydrocarbon feed to produce a steam cracking feedstock; and cracking hydrocarbons of the steam cracking feedstock and hydrocarbons of the light-end stream to produce one or more olefins; wherein the processing of the heavy hydrocarbon feed comprises: distilling the heavy hydrocarbon feed via vacuum distillation to produce a vacuum distillation residue and a vacuum distilled hydrocarbon stream; processing the vacuum distilled hydrocarbon stream via liquid-liquid extraction to produce a poly-aromatics stream comprising primarily poly-aromatics and an intermediate stream comprising paraffinic, aromatic, and naphthenic hydrocarbons; and hydroprocessing the intermediate stream to produce the steam cracking feedstock; wherein a used lubricating oil is lubricating oil that has partially or completely lost its capability of reducing the friction, heat, and wear between mechanical components after a period of usage, and/or lubricating oil that has accumulated contaminants after a period of usage. distilling the heavy hydrocarbon feed via vacuum distillation to produce a vacuum distillation residue and a vacuum distilled hydrocarbon stream; processing the vacuum distilled hydrocarbon stream via liquid-liquid extraction to produce a poly-aromatics stream comprising primarily poly-aromatics and an intermediate stream comprising paraffinic, aromatic, and naphthenic hydrocarbons; and hydroprocessing the intermediate stream to produce the steam cracking feedstock; wherein a used lubricating oil is lubricating oil that has partially or completely lost its capability of reducing the friction, heat, and wear between mechanical components after a period of usage, and/or lubricating oil that has accumulated contaminants after a period of usage.