The size of primary challenge with lipopolysaccharide induces changes in the innate immune cells phenotype between pro-inflammatory and pro-tolerant states when facing a secondary lipopolysaccharide challenge. To determine the molecular mechanisms governing this differential response, we propose a mathematical model for the interaction between three proteins involved in the immune cell decision making: IRAK-1, PI3K, and RelB. The mutual inhibition of IRAK-1 and PI3K in the model leads to bistable dynamics. By using the levels of RelB as indicative of strength of the immune responses, we connect the size of different primary lipopolysaccharide doses to the differential phenotypical outcomes following a secondary challenge. We further predict under what circumstances the primary LPS dose does not influence the response to a secondary challenge. Our results can be used to guide treatments for patients with either autoimmune disease or compromised immune system.