Write the GAMS code of the given mathematical model.

Answer the following questions.

$1.$ What are the optimum Z value and decision variable values?

$($For Z$,$ x$\_1,$x$\_2,$x$\_3,$x$\_4,$x$\_5,$s$\_0,$s$\_1,$s$\_2$ specify the values separately$)$

$2.$ Which one$($s$)$ of the constraint$($s$)$ is$($are$)$ binding? Which is$($are$)$ non$-$binding? Why?

$3.$ What are the shadow prices for all constraints? What do they mean for this model? Specify one by one.

$4.$ What are the reduced costs for all variables? What do they mean for the model? Specify one by one.

$5.$ If the investment budget was $$90,000($instead of $$100,000),$ would the current optimal basic solution change? Why? If the current optimal basic solution changes, what are the new values?

$6.$ If Finco can earn interest at $10\%($instead of $\%8)$ per year by keeping uninvested cash in money market funds? Why? If the current optimal basic solution changes, what are the new values?

$7.$ If $$1$ invested in investment C required again a $$1$ cash outflow at time $0$ but returned $$1\mathrm{.}5$ at time $1,$ would the current optimal basic solution change? Why? If the current optimal basic solution changes, what are the new values?

$8.$ If there is a $6$th investment opportunity and the cash flow is: $$1$ invested in investment F required a $$1$ cash outflow at time $1$ and returned $$2$ at time $2,$ should Finco invest money on investment F$?$ Finco Investment Corporation must determine an investment strategy for the firm during the next three years. Currently $($time $0),$ $$100,000$ is available for investment. Investments A$,$ B$,$ C$,$ D$,$ and E are available. The cash flow associated with investing $$1$ in each investment is given in Table.

For example, $$1$ invested in investment B requires a $$1$ cash outflow at time $1$ and returns $50$ at time $2$ and $$1$ at time $3.$ To ensure that the company$$s portfolio is diversified, Finco requires that at most $$75,000$ be placed in any single investment. In addition to investments A$$E$,$ Finco can earn interest at $8\%$ per year by keeping uninvested cash in money market funds. Returns from investments may be immediately reinvested. For example, the positive cash flow received from investment C at time $1$ may immediately be reinvested in investment B$.$ Finco cannot borrow funds, so the cash available for investment at any time is limited to cash on hand. Formulate an LP that will maximize cash on hand at time $3.$