Objective function: after-tax income is z = 4.3% * x1+5.4% * x2 * 50%+5.0% * x3 * 50%+4.4% * x4 * 50%+4.5% * X5.
Constraints:
1)x2+x3+x4 & gt； =400
2)2x 1+2 x2+x3+x4+5x 5 & lt； = 1.4( 1+x2+x3+x4+X5)
3)9x 1+ 15x 2+4x 3+3 x4+2x 5 & lt； =5(x 1+x2+x3+x4+x5)
4)x 1+x2+x3+x4+X5 & lt； = 1000
Where x 1, x2, x3, x4, x5 & gt=0.
1) Substitute the above model into Lingo, and the solution is: x1= 218.18; x2 = 0； x3 = 736.36x4 = 0； X5 = 45.45 The optimal income is 298,400 yuan.
2) According to the sensitivity analysis report, under the current optimal situation, for every increase of 1 unit investment, the income will increase by 2.98%, which is higher than the borrowing rate, and the increase is infinite. Therefore, managers borrow and invest as much as possible.
3) According to the sensitivity analysis report, under the current investment situation, there is no need to change the investment when the pre-tax income of Securities A increases to 4.65% or decreases to 3%. 4.5% is within this range.
The pre-tax income of securities C is between 4.889% and 8.467%, and there is no need to change the investment. However, if the pre-tax income of securities C is reduced to 4.8%, the investment will change accordingly.