Question

Jason's Jogging Shoes owns factories in three towns (A, B, and C), which distribute to three shops in three other cities (D, F, and G). The following table summarizes factory availabilities, projected store demands, and unit shipping costs:

From/To	Shop D	Shop F	Shop G	Factory Availability
Factory A	4	3	3	35
Factory B	6	7	6	50
Factory C	8	2	5	50
Store Demand	30	65	40

A. Do you think the problem shown is balanced?

B. Find out the optimal solution for shipping at Jason's Jogging Shoes.

Answer 1

A.

Yes the problem is balanced as total demand = total supply

B.

Let,

xij = number pf units transferred from factory i to shop j where i = {A,B,C and j = {D,F,G}

Objective is to minimize shipping cost so Objective function = Min 4x11+3x12+3x13+6x21+7x22+6x23+8x31+2x32+5x33

Subject to,

x11+x12+X13 <= 35 (Capacity - Factory A)
x21+x22+X23 <= 50 (Capacity - Factory B)
x31+x32+X33 <= 50 (Capacity - Factory C)

x11+x21+X31 = 30 (Demand - shop D)
x12+x22+X32 = 65 (Demand - shop F)
x13+x23+X33 = 40 (Demand - shop G)

xij >= 0 (non-negativity constraint)

Solving in solver we get following transportation schedule

Factory\Shop	D	F	G
A	0	15	20
B	30	0	20
C	0	50	0

Total minimized cost = 505

Solver screenshot

Solver formula