Solve the quadratic programming model (Equations 11.1 through 11.3) formulated for Example 11.2. What is the optimal investment policy for the Lion County Bank?

Equations 11.1 through 11.3:

Example 11.2 

Lion Country Bank is planning to expand into a new city by opening full-service branches, in-store branches, and ATMs. Management is willing to invest up to $7 million to establish a presence in this city if the overall return is better than 10% and need to know the investment risk.
Based on market research and prior experience, they have estimated the required investments, expenses, and returns as shown in Table 11.3.
Geographical diversification offers potential for reducing risk. The variance–covariance matrix of returns on investment for the 11 potential sites is given in Table 11.4. Note that the first three indices are for full-service sites, followed by the next three for store sites, and the last five for ATM sites.

Transcribed Image Text:

N N Minimize Risk = xQx=xx (11.1) 1=1]=1 Subject to ,x,Ret = 10% (Average returns on investments) (11.2) |=1 N J=1 ax, B (Maximum investment) (11.3)