Professor Proof is reconsidering where to invest the $50,000 left in his retirement account.

One available bond fund with estimated return of 5% per year has a published risk rating of 20.

The other option is a hedge fund with estimated return of 15% per year but a risk rating of 80 (it may be a ponzi scheme). Proof wants to divide his entire account between the two, placing no more that $40,000 in either fund. Within these limits he would like to both maximize total annual return and minimize the weighted (by investment size)

average of the risk ratings.

(a) Formulate Professor Proof’s problem as a multiobjective linear program with one main constraint, two upper bounds, and two nonnegativities. Be sure to define all decision variables and annotate objectives and constraints to show their meanings.

(b) Now show how to modify your formulation of

(a) as a goal program with targets of $6,000 annual return and a weighted risk average of 50. Weight shortfalls from the targets equally in the objective. Define all new decision variables and annotate new objectives and constraints to show their meanings.

(c) Enter and solve your goal program of (b)

with class optimization software.