An investment adviser currently has two types of investments available for clients: an investment

A that pays $4\%$ per year and an investment B of higher risk that pays $10\%$ per year. Clients may

divide their investments between the two investments to achieve any total return desired

between $4\%$ and $10\%.$ However, the higher the desired return, the higher the risk.

a$)$ Establish a mathematical model

b$)$ Write the matrix equation and for the model and find the inverse matrix

c$)$ How should each client listed in the table above invest to achieve the indicated return?