It aims to study the production and emission reduction decisions of production enterprises under carbon constraints. In the case of carbon constraints in production, manufacturers have four strategic choices: production within the carbon quota, adopting emission reduction technologies, purchasing carbon emission rights, and using emission reduction technologies and purchasing carbon emission rights. Based on the income model of production enterprises under four different strategies, first, under the condition of maximizing the interests of production enterprises, the optimal profit, optimal production, optimal total carbon emission, and optimal emission reduction rate under different carbon constraints are determined, and summarize its laws. Afterward, in order to further optimize corporate profits, the impact of changes in the carbon reduction scale cost and consumers’ low-carbon preference was studied. Several important conclusions are shown as follows. First, the stricter the carbon constraint policy, the greater the optimal emission reduction rate of enterprises. Second, the adoption of emission reduction technology can effectively reduce the impact of carbon constraint on output. Third, the optimal strategy is to both reduce emissions and purchase carbon emission rights, which can realize environmental economic dividends. Fourth, the lower the cost factor of the carbon reduction scale and the higher the low-carbon preference of consumers, the easier it is for firms to achieve carbon sufficiency in their production.