With the drastic consequences of climate change, such as increased global temperatures and rising sea levels, becoming more prevalent, the importance of reducing greenhouse gas emissions is heightened. One of the primary steps necessary to address this global environmental issue is to achieve net-zero emissions by adopting technologies that capture and sequester greenhouse gases. CO2 capture and utilization (CCU) stands out as one of the feasible strategies in mitigating and combatting climate change. This is because its characteristic of reusing and turning captured CO2 into valuable products addresses the economic drawbacks of CO2 capture and storage (CCS). This economic benefit incentivizes CO2 capture. To efficiently capture and utilize CO2 from power plant sources, decision support tools are necessary for the optimal planning and design of CCU systems. In this work, a linear programming (LP) model for matching CO2 sources and utilization facilities in a CCU system is developed, considering CO2 discounting, purity requirements, and material balance constraints. Purity or quality stipulations are necessary in the field of CCU since utilization facilities set purity standards before captured CO2 can be used in their processes. CO2 discounting, on the other hand, is included to quantitatively consider the effective CO2 emissions resulting from the delay made by various CCU industries or technologies. While CCU does not reduce the total amount of emissions like CCS, delaying the release of CO2 into the atmosphere is considered more beneficial than its direct emission. CCU can also be integrated with CCS so that more flexible systems with a wider array of options to achieve net-zero emissions can be generated. The developed model is then applied to a realistic CCU system case study to generate insights into the use of the model and its results. Using a conservative social discount rate of 5% on a CCU system with eight CO2 sources and four utilization facilities, an objective value of 2,639.70 monetary units and a CO2 discounting equivalent to 1.01 years were obtained from the model.