The California Department of Transportation (Caltrans) is looking to replace an aging highway overpass. The work requires closing two lanes of the highway, which causes traffic delays, and hence on-time completion of the project is critical. If the contractor who is awarded the project works diligently, the project is completed on time with probability 0.9. However, the contractor can slack off to save $10M in overtime costs, in which case the project is completed on time with probability 0.1.

Caltrans offers a contract that consists of a base payment and a bonus for on-time completion. Assume that the base payment is large enough so that the contractor would sign the contract given any of the bonuses listed below.

Of the bonuses listed below, which is the smallestthat still motivates the risk-neutral contractor to work diligently?

a)$9M

b) $7M

c)$5M

d) $11M

e) $13M