A bond portfolio manager has $$100,000$ to allocate to two different

bonds: one corporate bond, and one government bond.

The corporate bond has a yield of $4\%,$ a maturity of $3$ years and an A rating from a rating agency.

For computational purposes, this A rating translates into a numerical rating of $2.$ By contrast,

the government bond has a yield of $3\%,$ a maturity of $4$ years and rating of Aaa, which has

a corresponding numerical rating of $1.($Lower numerical ratings correspond to higher quality

bonds$).$A bond portfolio manager has $$100,000$ to allocate to two different

bonds: one corporate bond, and one government bond.

The corporate bond has a yield of $4\%,$ a maturity of $3$ years and an A rating from a rating agency.

For computational purposes, this A rating translates into a numerical rating of $2.$ By contrast,

the government bond has a yield of $3\%,$ a maturity of $4$ years and rating of Aaa, which has

a corresponding numerical rating of $1.($Lower numerical ratings correspond to higher quality

bonds$).$