This model included variables for production, ending inventory, demand allocation and then briefly, shipments between facilities as well as backlog/unmet demand. Extend this model to include the concern of tracking inventory and balance of parts (P1, P2, and P3) used in the manufacturing process. The data you'll need is:

PRODUCT	FACILITY	QTY
M1	F1	5
M2	F1	5
M3	F1	7
M1	F2	3
M2	F2	5
M3	F2	5

SHIP_ID	PART	FACILITY	DELIV_DATE	TIM_PERIOD	QTY
S12	P1	F1	1/1/21	1	15
S13	P1	F1	1/5/21	1	10
S14	P2	F1	1/8/21	2	15
S15	P3	F1	1/3/21	1	25
*** Before data feed to LP/MIP model, there would need to be an aggregation of ship_ids for a given part in a tim_period
*** Example: Shipments S12 & S13 are both for P1 arriving F1 in TIM_PERIOD 1 so the feed would be 25 units

PRODUCT	PART	QTY
M1	P1	1
M1	P2	1
M1	P3	1
M2	P1	3
M2	P3	1
M3	P1	1
M3	P2	1
M3	P3	1

A. Write high-level perspective of the interest. SUPPLY = DEMAND => ??? b. What variable(s) would need to be added for this extension other than below? PROD(time, prod, loc) = units of product made at location in a time period PROD(1, M1, F1) = units of product M1 made at F1 in period 1 c. What constraint(s) would need to be added for this extension?