The DotCom Corporation is implementing a pension plan for its employees. The company intends to start funding the plan with a deposit of $$50,000$ on January $1,2015.$ It plans to invest an additional $$12,000$ one year later, and continue making additional investments $($increasing by $$2,000$ per year$)$ on January $1$ of each year from $2017$ through $2029.$ To fund these payments, the company plans to purchase a number of bonds. Bond $1$ costs $$970$ per unit and will pay a $$65$ coupon on January $1$ of each year from $2016$ through $2019$ plus a final payment of $$1,065$ on January $1,2020.$Bond $2$ costs $$980$ and will pay a $$73$ coupon on January $1$ of each year from $2016$ through $2025$ plus a final payment of $$1,073$ on January $1,2026.$ Bond $3$ costs $$1,025$ and will pay an $$85$ coupon on January $1$ of each year from $2016$ through $2028$ plus a final payment of $$1,085$ on January $1,2029.$ The company's cash holdings earn an interest rate of $4\mathrm{.}5\%.$ Assume the company wants to purchase bonds on January $1,2015,$ and may buy them in fractional units. How much should the company invest in the various bonds and cash account to fund this plan through January $1,2029$ in the least costly way?a$.$ Create a spreadsheet model for this problem and solve it$.$b$.$ What is the optimal solution?