Question

Problem One A heavy trucks coompany has two warehouses in Muscat and Sohar and dealerships in Salalah and Alburaimi city. Every truck that is sold at the dealerships must be delivered from one of the warehouses. On a certain duy the Salalah dealers sell 10 trucks, and the Alburaimi city dealers sell 12. The Muscat warehouse has 15 trucks available, and the Sohar warchouse has 10. The cost of shipping one truck is 50 OMR from Muscat to Salalah, 40 OMR from Muscat to Alburaimi city, 60 OMR from Sohar to Salalah, and 55 OMR from Sohar to Alburaimi city. How many trucks must be shifted from each warebouse to each dealership in order to satisfy the orders at the minimum cost?

Answer 1

Transportation Cost:

Particulars	Salalah	Alburaimi	Supply
Muscat	50	40	15
Sohar	60	55	10
Demand	10	12

Minimum Cost:

The least cost of transportation is from Muscat to Alburaimi = 40 OMR

Hence, the maximum possiblee trucks must be shifted from Muscat to Alburaimi = 12 trucks

Cost = 12 * 40 = 480 OMR

Next least cost is from Muscat to Salalah = 50 OMR

However, the available trucks at Muscat = 3 (15-12)

Cost = 3 * 50 = 150 OMR

Next minimum cost is from Sohar to Alburaimi = 55 OMR

But, Alburaimi's demand has already been met by trucks from Muscat Warehouse

Hence, the balance trucks required must be shifted from Sohar to Salalah

Number of Trucks required = 7 (10-3)

Cost of shifting per truck= 60 OMR

Cost incurred = 7 * 60 = 420 OMR

Hence, Total Cost = 480 + 150 + 420

= 1,050 OMR

Conclusion: Number of Trucks to be transported

Particulars	Salalah	Alburaimi
Muscat	3 trucks * 50 OMR = 150 OMR	12 trucks * 40 OMR = 480 OMR
Sohar	7 trucks * 60 OMR = 420 OMR	NIL

Hence, the minimum cost = 1,050 OMR