Question

An e-commerce company located in Columbia, Missouri is considering two ways to deliver customer orders. The first option is to ship the goods directly to customers throughout the US using trucks. The second option is to ship the goods to a 3PL in Minneapolis, MN via rail and have them ship the goods to customers using the best mode of transportation. Given the data below for 500,000 units, please answer the following questions:

(a) what is the equivalence point of the two options in units?

(b) What is the total cost associated with the first option at a quantity of $200,000 units?

(c) what is the total cost associated with the second option at a quantity of $200,000 units?

(d) At which volumes should each option be used?

	Option 1 - ship directly from Columbia, MO to customers	Option 2 - ship from Columbia, MO to Minneapolis, MN by rail and then ship to customers using the best mode of transportation
Cost of material handling in Columbia, MO	$40,000	$0
Cost of transportation via rail	$360,000	$0
Cost of transportation via truck	$0	$250,000
Cost of transportation via air	$0	$ 50,000
Order fulfillment fee charged by 3PL	$0	$ 20,000
Fixed Cost	$20,000	$36,000

		a) equivalence point = 100,000 units b) total cost of option 1 at 200,000 units = $180,000 c) total cost of option 2 at 200,000 units = $164,000 d) At volumes less than 100,000 units, option 1 is the better option, whereas at volumes greater than 100,000 units, option 2 is the better option.
		a) equivalence point = 150,000 units b) total cost of option 1 at 200,000 units = $72,000 c) total cost of option 2 at 200,000 units =  $90,000 d) At volumes less than 150,000 units, option 1 is the better option, whereas at volumes greater than 150,000 units, option 2 is the better option.
		a) equivalence point = 200,000 units b) total cost of option 1 at 200,000 units = $150,000 c) total cost of option 2 at 200,000 units =  $220,000 d) At volumes less than 200,000 units, option 2 is the better option, whereas at volumes greater than 200,000 units, option 1 is the better option.
		a) equivalence point = 300,000 units b) total cost of option 1 at 200,000 units = $450,000 c) total cost of option 2 at 200,000 units =  $550,000 d) At volumes less than 300,000 units, option 2 is the better option, whereas at volumes greater than 300,000 units, option 1 is the better option.

Answer 1

Option 1

variable cost = 400,000

units = 500,000

per unti = .80 per unit

fixed cost 20,000

Option 2

variable cost = 320,000

per unit = .64 per unit

fixed cost 36,000

a) equivalent point is nothing but indifference point = difference in fixed costs / difference in variable costs

hence (36000-20000)/(0.80-0.64)

i.e 100,000 units

b) total cost at option 1 at 200000 units

variable cost = 200,000* .80 = 160,000

fixed cost = 20,000

Total 180,000

c) total cost at option 2 at 200,000 units

variable cost = 200,000*0.64 = 128,000

fixed cost = 36,000   

Total 164,000

d) if sales quantity above the indifference point or equivalent point least variable cost option is better in the given scenario option 2 has least variable cost hence option 2 is better if sales greater than 100,000 quantity

if sales less than 100,000 quantity I.e less than equivalent point then option with least fixed cost I.e option 1 where fixed are lower can be better