Im trying to integrate mathematical modelformulation into lingo but im getting syntax errors what are my mistakes and how can i correct them. Please provide me the correct runnable code.

Formulation of model:Qt$=$ Number of cars to be produced in period t$,$ t$=1,...,4.$

It$=$ Inventory level of cars at the end of period t$,$ t$=1,...,4.$

zt$=1$ if production is initiated in period t$,$ and $=0$ otherwise. $($Binary$)$

Dt$=$ Assumed demand forecasts for the next $4$ months are, $200,250,230$ and $210$ respectively.

ht$=$ $$500$ per car per month. The cost of storing an unsold car in month t$,$ t$=1,...,4.$

At$=$ $$500$ per setup at month t$,$t$=1,...,4.$

ct$=$ $$15,000$ per car

Min Z$=[(500)*($z$1)+(15,000)*($Q$1)+(500)*($I$1)+(500)*($z$2)+(15,000)*($Q$2)+(500)*($I$2)+(500)*($z$3)+(15,000)*($Q$3)+(500)*($I$3)+(500)*($z$4)+(15,000)*($Q$4)+(500)*($I$4)]$

Subject to:

I$1=0+$Q$1-200$

I$2=$ I$1+$Q$2-250$

I$3=$ I$1+$Q$2-230$

I$4=$ I$1+$Q$2-210$

$($I$0$ is assumed to to be zero$)$

Qzt

Qzt

Qzt

Qzt

It$,$ Qt $>=0$ t$=1,2,3,4$

zt in $\{0,1\}$ for each period t$=1,2,3,4$

Lingo Code:

SETS:

TIME $/1.\mathrm{.}4/$;

$!$ Define parameters for each period directly;

DATA:

Demand$(1)$ :$=200$;

Demand$(2)$ :$=250$;

Demand$(3)$ :$=230$;

Demand$(4)$ :$=210$;

$!$ Define constants;

SetupCost :$=500$;

UnitProdCost :$=15000$;

HoldingCost :$=500$;

VARIABLES:

Q$($TIME$)>=0$; $!$ Number of cars to be produced in each period;

I$($TIME$)>=0$; $!$ Inventory level at the end of each period;

z$($TIME$)$ binary; $!1$ if production is initiated, $0$ otherwise;

$!$ Objective function to minimize total costs;

MIN $=$ @SUM$($TIME: SetupCost $*$ z$($TIME$)+$ UnitProdCost $*$ Q$($TIME$)+$ HoldingCost $*$ I$($TIME$))$;

$!$ Inventory balance constraints;

@FOR$($TIME:

IF$($TIME $=1)$ THEN

I$(1)=$ Q$(1)-$ Demand$(1)$;

ELSE

I$($TIME$)=$ I$($TIME$-1)+$ Q$($TIME$)-$ Demand$($TIME$)$;

ENDIF;

$)$;

$!$ Ordering link constraint ensuring that orders only occur if indicated by z$($TIME$)$;

@FOR$($TIME:

Q$($TIME z$($TIME$)$;

$)$;

$!$ Set initial inventory to zero;

I$(0)$ :$=0$;

MODEL:

END;

Lingo Model $-$ Lingo$1$

SETS:

TIME $/1.\mathrm{.}4/$;

$!$ Define parameters for each period directly;

DATA :

Demand$(1)$ :$=200$;

Demand $(2)$ :$=250$;

Demand $(3)$ :$=230$;

Demand $(4)$ :$=210$;

$!$ Define constants;

SetupCost :$=$ :$=00$;

UnitProdCost :$=15000$ ;

HoldingCost :$=500$;

VARIABLES:

Q$($TIME$)0$; $!$ Number of cars to be produced in each period;

I $($TIME$)0$; $!$ Inventory level at the end of each period;

z $($TIME$)$ binary; $!$ l if production is initiated, $0$ otherwise;

$!$ Objective function to minimize total costs;

MIN $=$ @SUM$($TIME: SetupCost $*$ TIME$)+$ UnitProdCost $*Q(TIME)+$ HoldingCost $*$ I$($TIME$))$;

$!$ Inventory balance constraints;

IF $($TIME $=1$ THEN

$I(1)=Q(1)-$ Demand $(1)$;

ELSE

$I(TIME)=I(TIME-1)+Q(TIME)-$ Demand $($TIME$)$;

ENDIF;

;

$!$ Ordering link constraint ensuring that orders only occur if indicated by z$($TIME$)$;

@FOR $($TIME:

$Q(TIME)10000*z($TIME$)$;

; Lingo Model $-$ Lingo$1$

$S$ Lingo Model $-$ Lingo$1$

MODEL :

END;