Barney’s cousin, Bette Briggs, has been impressed by his bank’s portfolio management and has decided to avail herself of their expertise. Bette has informed the bank that she wants a return of 13% on her investment and she has been given details of three stocks X, Y and Z with average annual returns of 13.2%, 17.5%, and 9.7% respectively. Statistical information on these stocks is as follows: variances for X, Y, Z are 0.0012, 0.0023, and 0.00047, while covariances are XY =

–0.00019, XZ = 0.0009, and YZ = 0.000125. Using the investment model for Barney Briggs’s portfolio, find the percentage investments for X, Y and Z that will give Bette an overall return of 13%.