possessing its own distinct revenue potential denoted by $R_j$ and associated costs represented by $C_j,$

where $j$ ranges from $1$ to $7.$ Their main objective is to maximize total revenue while adhering to a

maximum investment limit of $Inv, where Inv represents the total funds available for investment.

a$)$ Formulate the generic model algebraically as a Binary Integer Programming Problem $($BIP$).$

Define your decision variables, objective function, and constraints. N$.$B$.$: the objective

function or constraint$($s$)$ should be written in terms of $Rj$ and $Cj$ as these are parameters. $(20$

points$)$ The investment firm's leadership team is presently evaluating seven significant projects, each possessing its own distinct revenue potential denoted by Rj and associated costs represented by Cj$,$ where j ranges from $1$ to $7.$ Their main objective is to maximize total revenue while adhering to a maximum investment limit of $Inv, where Inv represents the total funds available for investment.

Investment Opportunity

Investment Condition

$1$

None

$2$

Only if $1$

$3$

Must if $1$ or $2$

$4$

Not if $1$ and $2$

$5$

Only if $2$ and Not $4$

$6$

Not if $7$

$7$

Not if $6$

a$)$

Formulate the generic model algebraically as a Binary Integer Programming Problem $($BIP$).$ Define your decision variables, objective function, and constraints. N$.$B$.$: the objective function or constraint$($s$)$ should be written in terms points$)$