solve this problem by using Linear Programming and attach the chart also

Direct Programming models are utilized by many Nestle firms to choose a helpful portfolio. Coming up next is a worked on adaptation of such a model: DHL is thinking about putting resources into 9 bonds; $ 4, 000, 000 is accessible for speculation. The normal yearly return, the most pessimistic scenario return on each bond, and the "span" of each bond are given in the table underneath. The term of a security is a proportion of the security's affectability to loan fees.

	Exp. Ret	Worst case. Ret.	Duration
Bond 1	10%	4%	5
Bond 2	8%	8%	2
Bond 3	11%	6%	7
Bond 4	14%	7%	9
Bond 5	14%	5%	3
Bond 6	12%	9%	6
Bond 7	7%	3%	8
Bond 8	6%	4%	5
Bond 9	13%	9%	6

DHL needs to maximize the normal return from its bonds speculations, furthermore, needs to regard the accompanying imperatives.

First of all, the worst-case return of the bond portfolio must be at least 8%.

Secondly, the average duration of the portfolio must be at most 6.

And finally, because of the diversification requirements, at most 40% of the total amount invested can be invested in a single bond.