Please help solve this case study for my business analytics class:

The CFO at Performance Lawn Equipment, Brian Ferguson, wishes to design a minimum variance portfolio of index funds to invest some of the firm's cash reserves. The funds selected for consideration and their variance-covariance matrix and average returns are given in the table below.

a. The firm would like to achieve a target return of 0.19%. What mix of investments would achieve this?

b. To obtain better diversification, the CFO would like to restrict the percentage of investments in each fund as follows:

BOND: between 10% and 50%

S&P 500: between 30% and 50%

SMALL CAP: no more than 20%

MID CAP: no more than 20%

LARGE CAP: no more than 25%

EMERGING MARKET: no more than 10%

COMMODITY: no more than 20%

How would the optimal portfolio and objective change? Summarize your findings in a short memo to Mr. Ferguson

	Bond	S&P 500	Small Cap	Mid Cap	Large Cap	Emerging Market	Commodity
Bond	0.002%
S&P 500	-0.001%	0.020%
Small Cap	-0.001%	0.027%	0.047%
Mid Cap	-0.001%	0.024%	0.039%	0.033%
Large Cap	-0.001%	0.019%	0.027%	0.023%	0.027%
Emerging market	0.000%	0.032%	0.050%	0.043%	0.041%	0.085%
Commodity	0.000%	0.000%	0.005%	0.005%	0.009%	0.015%	0.054%
Avg Weekly Return	0.044%	0.118%	0.256%	0.226%	0.242%	0.0447%	0.053%