help me step by step in excel solver$6\mathrm{.}3$ Selecting an Investment Portfolio: An investment manager wants to determine an

optimal portfolio for a wealthy client. The fund has $$2\mathrm{.}5$ million to invest, and its objective is to

maximize total dollar return from both growth and dividends over the course of the coming year.

The client has researched eight high$-$tech companies and wants the portfolio to consist of shares

in these firms only. Three of the firms $($S$1$S$3)$ are primarily software companies, three $($H$1$H$3)$

are primarily hardware companies, and two $($C$1$C$2)$ are Internet consulting companies. The

client has stipulated that no more than $40\%$ of the investment be allocated to any one of these

three sectors$.$ To ensure diversification, at least $$100,000$ must be invested in each of the eight

stocks. Moreover, the number of shares invested in any stock must be a multiple of $1000.$

The table below gives estimates from the investment company$$s database relating to these stocks.

These estimates include the price per share, the projected annual growth rate in the share price,

and the anticipated annual dividend payment per share.

Stock

S$1$ S$2$ S$3$ H$1$ H$2$ H$3$ C$1$ C$2$

Price per share $$40$ $$50$ $$80$ $$60$ $$45$ $$60$ $$30$ $$25$

Growth rate $0\mathrm{.}050\mathrm{.}100\mathrm{.}030\mathrm{.}040\mathrm{.}070\mathrm{.}150\mathrm{.}220\mathrm{.}25$

Dividend $$2\mathrm{.}00$ $$1\mathrm{.}50$ $$3\mathrm{.}50$ $$3\mathrm{.}00$ $$2\mathrm{.}00$ $$1\mathrm{.}00$ $$1\mathrm{.}80$ $$0\mathrm{.}00$

a$.$ Determine the maximum return on the portfolio. What is the optimal number of shares to

buy for each of the stocks? What is the corresponding dollar amount invested in each stock?

b$.$ Compare the solution in which there is no integer restriction on the number of shares

invested. By how much $($in percentage terms$)$ do the integer restrictions alter the value of the

optimal objective function? By how much $($in percentage terms$)$ do they alter the optimal

investment quantities?