The globally optimal design and operation of a process that converts a hybrid waste tire and natural gas feedstock to multiple products (such as electricity, methanol, dimethyl ether, olefins, and liquefied natural gas) as part of a polygeneration scheme is presented. A three-step methodology is followed: First, rigorous process models for the mass and energy balance calculations are implemented; next, these models are sampled to generate data that are used to fit surrogate models which take the form of algebraic equations relating input and output variables for each process section; lastly, a Mixed-Integer Nonlinear Program that maximizes net present value is formulated using the recently developed GOSSIP software and solved with the linked ANTIGONE solver. The optimal product portfolio under a variety of market and policy scenarios is presented for two cases: Without and with waste tire tipping fees of 100 $/tonne. Furthermore, the synergies between the waste tire and natural gas feedstocks are investigated. The optimal product portfolio is found to be highly sensitive to prevailing market conditions thus motivating future work on design under uncertainty of flexible polygeneration processes that are able to change operating conditions in response to varying prices.