Faraday Corporation must determine how many devices should be produced during each of the

next four quarters. Demand is as follows:

Quarter $1$ : $70$ units;

Quarter $2$ : $70$ units;

Quarter $3$ : $80$ units;

Quarter $4$ : $80$ units.

At the beginning of the first quarter, the company has $25$ devices in the inventory. During each

quarter, Faraday can produce up to $40$ devices at a cost of $$1000$ per device using regular employee

hours. By having employees work overtime during a quarter, it can produce additional $30$ devices

at a cost of $$1500$ per device. Faraday Corporation can also purchase up to $10$ device$/$month from

a subcontractor at a cost of $$1450/$device$.$ It costs $$50$ per quarter to hold a device in inventory.

Demand can be backlogged at a cost of $$100/$device$/$quarter$.$

Formulate a balanced transportation problem $($Tableau and LP$)$ to minimize the sum of production,

inventory, backlogging, purchasing costs during the next four quarters