Question

WRITE OBJECTIVE FUNCTION AND CONSTRAINTS.

A soft drink manufacturing company has 3 factories—one in Orlando, one in Tampa, and one in Port St. Lucie—which supply soft drink bottles to 3 warehouses located in the city of Miami. The associated per-unit transportation cost table is provided below.

Transportation Costs ($)
Factories/Warehouse (W)	W1	W2	W3
Orlando	4	3	7
Tampa	7	6	4
Port St. Lucie	3	6	6

The factory in Orlando has a capacity of 15,000 units.
The factory in Tampa has a capacity of 18,000 units.
The factory in Port St. Lucie has a capacity of 8,000 units.

The requirements of the warehouses are:

Warehouse	Requirement (Bottles)
W1	18,000
W2	12,000
W3	5,000

WRITE OBJECTIVE FUNCTION AND CONSTRAINTS.WRITE OBJECTIVE FUNCTION AND CONSTRAINTS.WRITE OBJECTIVE FUNCTION AND CONSTRAINTS.WRITE OBJECTIVE FUNCTION AND CONSTRAINTS.

Answer 1

Factories/Warehouse(W)				W1	W2	W3
Orlando				x11	x12	x13
Tampa				x21	x22	x23
Port St. Lucie				x31	x32	x33
Let x11 be the number of units to be transported from Orlando to W1, x12 be the transportation from Orlando to W2 and so on.
Similarly x21 be the transporataion from Tampa to W1 and so on.
and
Similarly x31 be the transporataion from Port St. Lucie to W1 and so on.
Objective is to minimize transportation cost.
Minimize transportation cost				=	4x11+3x12+7x13+7x21+6x22+4x23+3x31+6x32+6x33
Constraints:
Condition 1:Limiation of factory
	x11+x12+x13 < 15000
	x21+x22+x23 < 18000
	x31+x32+x33 < 8000
Condition 2:Limiatation of warehouse:
	x11+x21+x31 < 18000
	x12+x22+x32 < 12000
	x13+x23+x33 < 5000
Thus,
Objective,
Minimize (Z)		=	4x11+3x12+7x13+7x21+6x22+4x23+3x31+6x32+6x33
Subject to constrtaints,
	x11+x12+x13 < 15000
	x21+x22+x23 < 18000
	x31+x32+x33 < 8000
	x11+x21+x31 < 18000
	x12+x22+x32 < 12000
	x13+x23+x33 < 5000
	X11, x12 to x33 > 0