A financial advisor is about to build an investment portfolio for a client who has $400,000 to invest. The four investments available are A, B, C, and D. Investment A will earn four percent and has a risk of two "points" per $1,000 invested. Investment B earns six percent with five risk points; investment C earns nine percent with nine risk points; and investment D earns 11 percent with a risk of eighteen. The client has put the following conditions on the investments: 1) A is to be no more than 40 percent of the total invested; 2) A cannot be less than 20 percent of the total investment; 3) D cannot be less than C; and 4) Total risk points must be at or below 450.
Formulate this as a linear programming model, that is, i) define your decision variables, ii) state the objective function, iii) write down all of the constraints and put them in a standard LP format.