Question

UESTION 1 McTavish Transportation loads Intermodal containers onto railcars. Each railcar can accommodate a maximum size load of 60 feet long x 8 feet wide x 8 feet high. McTavish only loads three sized of intermodal containers: Short Standard Long 55 x 8 x 8 Container size (L x W x H) (in feet)10x8x 8 20 x 8 x8 $900 300 $520 280 $2,100 Price charged to customer: Variable cost per container 400 McTavish currently has space available on 10,000 railcars. No additional railcars are available. Fixed costs related to loading and the 10,000 railcars is $8,000,000 Various customers have the following containers to be loaded. Total demand is as follows: Short: 36,000 containers Standard:18,000 containers Long: 00 containers McTavish can pick and choose which containers are loaded and which customers to accept. Required How many rail cars would be required to satisfy all of the current demand? How many of each container type should McTavish load?

Answer 1

	Demand	Dimensions	Volume	Total Volume
Short	36,000	10 X 8 X 8	640	2,30,40,000
Standard	18,000	20 X 8 X 8	1,280	2,30,40,000
Long	3,000	55 X 8 X 8	3,520	1,05,60,000
Total Volume				5,66,40,000
Volume per rail car		60 X 8 X 8	3840
Number of railcars required				14,750

Volume = Length X Width X Height
Number of railcars = Total volume / Volume per rail car

In order to see each type of container that the company must load, we need to see the combination in which the total contribution is maximum. To see that we need to find out contribution per feet and rank them. Here contribution per feet = Contribution per container / Volume per container

	Demand	Dimensions	Volume per container	Total Volume	Price Charged	Variable Cost	Contribution per container	Contribution per feet	Ranking
Short	36,000	10 X 8 X 8	640	23,040,000	$                  520	$                280	$               240	0.375	III
Standard	18,000	20 X 8 X 8	1,280	23,040,000	$                  900	$                300	$               600	0.469	II
Long	3,000	55 X 8 X 8	3,520	10,560,000	$              2,100	$                400	$            1,700	0.483	I
Total Volume				56,640,000

Maximum space available = 10,000 X 60 X 8 X 8 = 38,400,000
Space required by long containers = 10,560,000
Space remaining = 38,400,000 - 10,560,000 = 27,840,000
Space required by standard containers (2nd ranking) = 23,040,000
Space remaining for Short containers = 27,840,000 - 23,040,000 = 4,800,000
Space required by 1 short container = 640
Number of containers = 4,800,000 / 640 = 7,500 containers

Total number of containers are as follows
1. Long = 3,000 containers
2. Standard = 18,000 containers
3. Short = 7,500 containers