The transport sector is the second largest carbon emissions contributor in Europe and its emissions continue to increase. Many producers are committing themselves to reducing transport emissions voluntarily, possibly in anticipation of increasing transport prices. In this paper we study a producer that has outsourced transport and has decided to cap its carbon emissions from outbound logistics for a group of customers. Setting an emission constraint for a group of customers allows for taking advantage of the portfolio effect. We focus on reducing emissions by switching transport modes within an existing network, since this has a large impact on emissions. In addition, the company sets the sales prices, which influence demand. The problem is solved by decomposing the multi-product problem into several single-product problems, which we then analyze separately. Using the single-product solutions we create an efficient frontier which reflects the trade-off between total carbon emissions and the total prot. It is observed that a diminishing rate of return applies in reducing emissions by switching transport modes. In a case study we apply our method to a producer of bulk liquids and find that emissions can be reduced by 10% at only a 0.7% increase in total logistics cost.