The insulin signaling pathway, when activated, both upregulates the activity of the mTORC1 pathway and inhibits the FOXO transcription factor.

a) Explain the role of insulin in glucose metabolism.
b) Describe the functions of mTORC1 in cellular processes.
c) Elaborate on the regulatory role of FOXO in cell survival.
d) Discuss the interplay between insulin, mTORC1, and FOXO.