The US Navy is hoping to reward its most capable new officers by offering one-time bonuses to new US Naval Academy graduates. If the graduate's final GPA is 3.5 or higher, the bonus is $50K; if it is 2.5 or higher, but below 3.5, the bonus is $10K, and if the GPA is below 2.5, there is no bonus at all. Assume that all officers are able to attain a GPA of 2.0 without exerting effort.

The effort cost of attaining a GPA,g, that is higher than 2.0 differs across the two types of officers. Forhighly capableofficers, attaining a GPA ofgcostsc_H(g)=5(g2)in effort. Forless capableofficers, the cost isc_L(g)=10(g2)in effort. Both effort costs are measured in thousands of dollars.

Assuming that students work to maximize bonus net of effort cost and that the Navy can only observe GPA (i.e., it can't directly observe how academically capable a student is).

Are the following statements true or false?

1.Highly capable officers will receive $50K bonuses.

2.Highly capable officers will receive $10K bonuses.

3.Less capable officers will receive $50K bonuses.

4.Less capable officers will receive $10K bonuses.

5. At least one of the officer types will fail to receive a bonus.