4. A finance company intend to invest 40,000 into three different schemes. All invest- ments must be in multiples of 10,000. Up to 20,000 can be invested in each scheme. The following table gives the expected return from each scheme. Investment Scheme 1 Scheme 2 Scheme 3 10,000 16,000 14,000 18,000 20,000 29,000 27,000 30,000 (a) Use dynamic programming to find the investment plan that maximises the return. No marks will be awarded if a method other than Dynamic Programming is used. Include all definitions in your answer. [20 marks] (b) State the Integer Programming formulation for this problem. (5 marks]