A bond portfolio manager holds three bonds in her portfolio. All the bonds have the same duration. Bond $1$ has a market value of $$25,000,000$ and a convexity of $2,$ Bond $2$ has a market value of $$13,300,000$ and a convexity of $8\mathrm{.}5,$ bond $3$ has a market value of $$32,343,000$ and a convexity of $13.$ Assume the portfolio manager strongly believes that interest rates will drop over the next six months. Which of the following actions would allow her to benefit most from this projected decrease in rates?

a$.$ Buy $$10,000,000$ worth of bond $3$ and sell more of bond $2$

b$.$ Buy $$10,000,000$ worth of bond $2$ and sell more of bond $1$

c$.$ Buy $$10,000,000$ worth of bond $1$ and sell more of bond $3$

d$.$ Buy $$10,000,000$ worth of bond $3$ and sell more of bond $1$