$1.$ You are responsible $of$ optimizing the multi period production planning $of$ a company. Down below you can find the parameters about capacity, costs and weekly orders. Please formulate $aLPto$ plan the production $of$ this company and write a CPLEX code. $On$ the second image; indices, decision variables and how the production looks like $on$ a weekly basis $is$ given $to$ you $as$ a hint.

$On$ the third image, you can find the CPLEX code for indices, parameters and decision variables. This $is$ given $to$ you $as$ a guide but you can code $in$ any way that you want.

Please formulate the model and the code $in$ the close form $as$ much $as$ possible. Production Capacity: $160$ computers per week

$50$ more computers with overtime

Assembly Costs: $\frac{?}{?}$$$190$ per computer regular time; $\frac{?}{?}$$$260$ per computer overtime Inventory Holding Cost: $\frac{?}{?}$$$\frac{10}{c}$omputer per week

Order schedule:$\frac{?}{b}$

egin$\{tabular\}\{|c|c|\}\frac{?}{h}$

line Week & $\frac{?}{\text{b}\text{e}\text{g}\text{i}\text{n}\{tabular\}\{c\}}$

Computer Orders$\frac{\frac{?}{?}}{?}$

$\frac{?}{(\frac{?}{\text{l}\text{e}\text{f}\text{t}(/mathrm\frac{\{d{\}}_{\frac{?}{\text{m}\text{a}\text{t}\text{h}\text{r}\text{m}\{i\}}}}{r}\text{i}\text{g}\text{h}\text{t})}\frac{?}{?})}\frac{?}{e}$

$nd\{tabular\}\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}1$ & $105\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}2$ & $170\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}3$ & $230\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}4$ & $180\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}5$ & $150\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}6$ & $250\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}\frac{?}{e}$

$nd\{tabular\}$ Production Capacity: $160$ computers per week

$50$ more computers with overtime

Assembly Costs: $\frac{?}{?}$$$190$ per computer regular time; $\frac{?}{?}$$$260$ per computer overtime Inventory Holding Cost: $\frac{?}{?}$$$\frac{10}{c}$omputer per week

Order schedule:$\frac{?}{b}$

egin$\{tabular\}\{|c|c|\}\frac{?}{h}$

line Week & $\frac{?}{\text{b}\text{e}\text{g}\text{i}\text{n}\{tabular\}\{c\}}$

Computer Orders$\frac{\frac{?}{?}}{?}$

$\frac{?}{(\frac{?}{\text{l}\text{e}\text{f}\text{t}(/mathrm\frac{\{d{\}}_{\frac{?}{\text{m}\text{a}\text{t}\text{h}\text{r}\text{m}\{i\}}}}{r}\text{i}\text{g}\text{h}\text{t})}\frac{?}{?})}\frac{?}{e}$

$nd\{tabular\}\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}1$ & $105\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}2$ & $170\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}3$ & $230\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}4$ & $180\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}5$ & $150\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}6$ & $250\frac{\frac{?}{?}}{?}$

$\frac{?}{\text{h}\text{l}\text{i}\text{n}\text{e}}\frac{?}{e}$

$nd\{tabular\}$

$r_j=$ regular production $of$ computers $in$ week $j$

$(j=1,2,$dots.,$6)$

$o_j=$ overtime production $of$ computers $in$ week $j$

$(j=1,2,$dots.,$6)$

$i_j=$ extra computers carried over $as$ inventory $in$ week $j$

$(j=1,2,$dots.,$5)$ int weekCount $=6$;

range week $=1..$weekCount;

int prodCap $=160$;

int overCap $=50$;

int regCost $=190$;

int overCost $=260$;

int invCost $=10$;

float Orders$[week]=...$;

dvar float$+r[week]$;

dvar float$+o[week]$;

dvar float$+i[week]$;

dexpr float $z=$ sum$(jin$ week$)((regCosti[j]))$;

minimize $z$;