PROBLEM #$1$: A production manager needs to develop a production schedule to meet the following demand:

Period

$1$

$2$

$3$

$4$

Demand

$500$

$1300$

$1600$

$500$

production costs are as follows:

production cost during regular time: $$4$ per unit

cost of subcontracting: $$5$ per unit

Inventory carrying cost $=$ $$3$ per unit per period

Back$-$order costs $=$ $$8$ per unit per period.

Regular production rate: $900$ units per period

You can subcontract at the rate of $150$ units per period only during the second and third periods. Develop a production schedule for this scenario and answer the following questions.

Equation: Surplus$/$Shortage in any period $=$ Quantity Produced $+$ Quantity Subcontracted $$ Demand

What is the average inventory for the first period?

What is the surplus or shortage in the second period?

What is the inventory at the beginning of the second period?

What is the average inventory for the second period?

What is the surplus or shortage in the third period?

What is the backlog for the third period?

What is the total cost of the items subcontracted during periods $2$ and $3$ together?

What is the total cost of carrying inventory for all the four periods together?

What is the total cost of the backlog for all the four periods together?

What is the total cost of meeting the demand for the four periods is: