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, 2018. 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 2020 through 2032. 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 2019 through 2022 plus a final payment of $1,065 on January 1, 2023. Bond 2 costs $980 and will pay a $73 coupon on January 1 of each year from 2019 through 2028 plus a final payment of $1,073 on January 1, 2029. Bond 3 costs $1,025 and will pay a $85 coupon on January 1 of each year from 2019 through 2031 plus a final payment of $1,085 on January 1, 2032. The company's cash holdings earn an interest rate of 4.5%. Assume the company wants to purchase bonds on January 1, 2018 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, 2032 in the least costly way? a. model for this problem and solve it. b. What is the optimal solution?