$1$st : Define Decision Variables

$x_1$ : nember of small rooms to add $x_2$ :$"."$ medium

$x_3$: $".$ "lange

$2$nd: Define thegoal constraints

Small Room: $x_1+d_1^{-}-d_1^{+}=5$

Medium $"$: $x_2+d_2^{-}-d_2^t=10$

Lengeroom: $x_3+d_3^{-}-d_3^{+}=15$

Chat : Here all are alse defined as non$-$negat ive decision veriables ta be solued for.

$7-)$ We want to expand the convention center in an hotel.

The types of conference rooms being considered are:

$\backslash$table$[[,$Size $(m^2),$Unit Cost$],[$Small $400,$$$18,000,],[$Medium $750,$$$33,000,],[$Large $1,050,$$$45,150,]]$

We would like to add $5$ small, $10$ medium and $15$ large conference rooms.

We also want the total expansion to be $25,000$ square meters and to limit the cost to $$1,000,000.$

Goal $1$: The expansion should include approximately $5$ small conference rooms.

Goal $2$: The expansion should include approximately $10$ medium conference rooms.

Goal $3$: The expansion should include approximately $15$ large conference rooms.

Goal $4$: The expansion should consist of approximately $25,000$ square meters.

Goal $5$: The expansion should cost approximately $$1,000,000.$

If all desired are done for the # of rooms, they need

$25,250$ sq$.$ meter

$$1,097,250$

If we accept, $25,000$ sq$.$ Meters and $$1,000,000$ as constraints, what it is the objective?

Total cost $($insiooos$)$: $18x_1+33x_2+45\mathrm{.}15x_3+d_s^{-}-d_s^{+}=1000$

where $x_1,x_2,d_i^{-}{d}_i^{+}0,$ so $x_1,x_2,x_3,d_1^{-}{d}_{1}t{d}_2^{-}{d}_2{d}_3^{-}{d}_3^{+}{d}_4^{-}{d}_4^{+}0d_{s^{-}}{d}_{5^{+}}$