Question

Newman has decided he is going to pursue the “bottle deposit scheme”. He and Kramer will collect cans and drive them to Saginaw Michigan where they will get the refund per can. The refund amount per can has just increased for the upcoming President’s Day weekend. The refund is now $0.20 per can. Newman knows with the short amount of time he has that only two options are available: the Uhaul plan and the Mailtruck plan. The underlying scheme is the same but the costs have shifted a bit.

The Uhaul plan consists of the following costs:

-    fixed rental costs for the Uhaul of $400
-    fixed gasoline costs of $1.99 a gallon for the 1,400 mile roundtrip excursion and they can expect to get about 17 miles per gallon with the Uhaul
-    variable costs of $0.02 per can but the Uhaul can easily handle 4000 cans before these costs kick in (i.e., Newman gets 4000 cans free before the variables costs start)

The Mailtruck plan consists of the following costs:

-    fixed rental costs for the Mailtruck of $0 [he gets it free for being a Postal Carrier]
-    fixed gasoline costs of $1.99 a gallon for the 1,400 mile roundtrip excursion and they can expect to get about 13 miles per gallon with the Mailtruck
-    variable costs of $0.06 per can as the Mailtruck is older and needs TLC so the variable costs are higher than the Uhaul --- In addition, it can only handle 2000 cans before these costs kick in (i.e., Newman only gets 2000 cans free before the variables costs start)

The variable costs for both plans consist of wear and tear on the vehicle as more cans are loaded in (i.e., oil, radiator fluid, etc.) and charges through the toll-ways (e.g., the Uhaul gets a different rating and pays less than the Mailtruck when passing through toll-ways). Answer the following questions based on a comparison of costs between the two plans.

a.    If Newman expects to collect around 6000 cans, which plan should he select?

b.    Perform an analysis based on the idea that Kramer believes they can collect around 6000 cans on average but they may collect as many as 8000 cans or as little as 4000 cans.

c.    How does the decision change if Kramer’s estimates increase to 10000 cans on average with a high end of 12000 cans or a low end of 8000 cans?

Answer 1

a) Newman should select mailtruck plan for 6000 cans.

Cans = 6000	Uhaul	Mailtruck
Fixed rental	$                        400.00	0
Gasoline cost = 1400 / Mileage (17 and 13 respectively) * 1.99	1400/17 * 1.99= $163.88	400/13 * 1.99= 214.31
Variable cost	$                          40.00	$                        240.00
	(Pays for 2000 cans)	(Pays for 4000 cans)
Total cost = Fixed rental + Gasoline cost + Variable cost	$                        603.88	$                        454.31

b) With the number of cans changing only cost that is effected is Variable cost. For the range of 4000-8000 with average of 6000, mail truck still remains a better option as per cost.

Cans = 4000	Uhaul	Mailtruck
Fixed rental	$                        400.00	0
Gasoline cost = 1400 / Mileage (17 and 13 respectively) * 1.99	$                        163.88	$                        214.31
Variable cost	0	$                        120.00
	(Pays for 0 cans)	(Pays for 2000 cans)
Total cost = Fixed rental + Gasoline cost + Variable cost	$                        563.88	$                        334.31
Cans = 8000	Uhaul	Mailtruck
Fixed rental	$                        400.00	0
Gasoline cost = 1400 / Mileage (17 and 13 respectively) * 1.99	$                        163.88	$                        214.31
Variable cost	$                          80.00	$                        360.00
	(Pays for 4000 cans)	(Pays for 6000 cans)
Total cost = Fixed rental + Gasoline cost + Variable cost	$                        643.88	$                        574.31

c) For lower end range of 8000, Mailtruck remains a better option. However, this range with an average of 10000 which can go upto 12000 should be served using Uhaul as the cost gets lower. Please see table below on how cost changes when cans are 8000, 10000 and 120000 respectively

Cans = 8000	Uhaul	Mailtruck
Fixed rental	$                        400.00	0
Gasoline cost = 1400 / Mileage (17 and 13 respectively) * 1.99	$                        163.88	$                        214.31
Variable cost	$                          80.00	$                        360.00
	(Pays for 4000 cans)	(Pays for 6000 cans)
Total cost = Fixed rental + Gasoline cost + Variable cost	$                        643.88	$                        574.31
Cans = 10000	Uhaul	Mailtruck
Fixed rental	$                        400.00	0
Gasoline cost = 1400 / Mileage (17 and 13 respectively) * 1.99	$                        163.88	$                        214.31
Variable cost	$                        120.00	$                        480.00
	(Pays for 6000 cans)	(Pays for 8000 cans)
Total cost = Fixed rental + Gasoline cost + Variable cost	$                        683.88	$                        694.31
Cans = 12000	Uhaul	Mailtruck
Fixed rental	$                        400.00	0
Gasoline cost = 1400 / Mileage (17 and 13 respectively) * 1.99	$                        163.88	$                        214.31
Variable cost	$                        160.00	$                        600.00
	(Pays for8000 cans)	(Pays for 10000 cans)
Total cost = Fixed rental + Gasoline cost + Variable cost	$                        723.88	$                        814.31