How to lower the cost of this with these parameters:

Maximum regular hours per worker per quarter $450$

Maximum overtime hours per worker per quarter $100$

Maximum number of workers $85$

Starting workforce $55$

Hiring cost per worker $2000$

Firing cost per worker $1400$

Regular time wage $30$

Overtime wage $45$

Subcontract Cost $125$

Back order cost $100$

Holding cost per pair of shoes per quarter $1$

Ending Inventory Period $0$: $3000$

Quarter $12345678$

Aggregate demand in order of quarters: $2624527110295103749049030518154080536845$

MIX AGGREGATE PLAN extra credit

Period $12345678$

Forecast $2624527110295103749049030518154080536845$

Production

Regular Time $303735837357382503825038250382503825038250$

Overtime $45$

Subcontract $125$

Total Production $3735737357382503825038250382503825038250$

Number of Workers $558383858585858585$

Inventory

Beginning $3000141122435933099338592307995146959$

Ending $30001411224359330993385923079951469598364$

Average $855619235\mathrm{.}528729334792846916296\mathrm{.}58236\mathrm{.}57661\mathrm{.}5$

Backlog

Labor Costs

Regular $3011207101120710114750011475001147500114750011475001147500$

Overtime $4500000000$

Subcontract $12500000000$

Hire $200056000$

Fire $1400$

Total Labor Cost $11767101120710114750011475001147500114750011475001147500$

Inventory Costs

Holding Cost $1855619235\mathrm{.}528729334792846916296\mathrm{.}58236\mathrm{.}57661\mathrm{.}5$

Back Order $10000000000$

Total Production Cost $11852661139945\mathrm{.}51176229118097911759691163796\mathrm{.}51155736\mathrm{.}51155161\mathrm{.}5$

Total Cost $$9,333,083\mathrm{.}00$

target: $9,055,000$