Question

Solve this linear programming (LP) problem using the transportation method. Find the optimal transportation plan and the minimum cost. (Leave no cells blank - be certain to enter "0" wherever required. Omit the "$" sign in your response.)

Minimize 8x11	+ 2x12 + 5x13 + 2x21 + x22
	+ 3x23 + 7x31 + 2x32 + 6x33

Subject to	x11 + x12 + x13	=	90
	x21 + x22 + x23	=	105
	x31 + x32 + x33	=	105
	x11 + x21 + x31	=	150
	x12 + x22 + x32	=	75
	x13 + x23 + x33	=	75
	All variables	≥	0

x11 =		x12 =		x13 =
x21 =		x22=		x23 =
x31 =		x32 =		x33 =
Total Cost =

Answer 1

ANS::

as for given data

Decision Variables:
Source/Destination	B1	B2	B3	Supply
A1	x11	x12	x13	90
A2	x21	x22	x23	105
A3	x31	x32	x33	105
Demand	150	75	75
Cost:
Source/Destination	B1	B2	B3
A1	$             8	$             2	$             5
A2	$             2	$             1	$             3
A3	$             7	$             2	$             6
LP Model:
Source/Destination	B1	B2	B3	Total	Sign	Supply
A1				0	=	90
A2				0	=	105
A3				0	=	105
Total	0	0	0
Sign	=	=	=
Demand	150	75	75
Total Cost	$           -

Solution:

x11 =	0	x12 =	15	x13 =	75
x21 =	105	x22 =	0	x23 =	0
x31 =	45	x32 =	60	x33 =	0
Total cost		$    1,050

thank you....