a phone maker is making a production plan for the coming financial year. Their collaborative forecast with service provider is as follows:

Month

Demand in $1000$s

Month

Demand in $1000$s

July

$1000$

January

$1600$

August

$1100$

February

$900$

September

$1000$

March

$1100$

October

$1200$

April

$800$

November

$1500$

May

$1400$

December

$1600$

June

$1700$

Since they oly assemble the phones from supplier$$s parts, capacity is only constrained by employees. The plant operates $20$ days a month, eight hours a day. A person can assemble phones every $10$ minutes. Workers are paid $800$ rupees per hour and $50\%$ overtime premium. The plant currently employees $1250$ employees. Component cost is $4000$ rupees. Inventory carrying cost of a phone is $500$ rupees a month. Seacell has no layoff policy and allows only $20$ hours of overtime per month per employee. They have a starting inventory of $40,000$ units and wants to the year with $50000$ units in inventory.

What is the optimum production schedule? $($No backorders and contracting$)?$ If they can increase overtime hours from $20$ to $30$ what will be the value for the company?

If the overtime remains at $20$ hours per employee, and a third party is willing to make the phone at rupees $4250,$ how will your production plan change?