Answer:
amount to be investment in risky portfolio =  $405
amount invest in security x = $243
amount invested in security Y = $162
Explanation:
given data 
investing = $1,000
Treasury bills = 5%
optimal weights of X = 60 %
optimal weights of Y = 40 %
expected rate of return x =  14%
expected rate of return y = 10%
solution
we know that 
                       weight                     return                     return from risky port 
X                     60 %                         14 %                       8.4 %
Y                     40 %                          10 %                       4%
total                                                                                 12.4 %
so here 
return from risky portfolio is = 12.4 %
and 
return from risk free investment = 5 % 
so 'we consider here investment in risky portfolio = x 
so investment in risk free  = 1 - x
so we can say that 
12.4 % × x + 5 % × (1-x) = 8 %
solve we get 
x = 0.405
so investment in risky portfolio = 0.405
so investment in risk free  =0.595
and
amount to be investment in risky portfolio = $1000 × 0.405
amount to be investment in risky portfolio =  $405
and
amount invest in security x = $405 × 60%
amount invest in security x = $243
and
amount invested in security Y = $405 × 60% 
amount invested in security Y = $162