Question 1118030: A manager is trying to decide whether to purchase a certain part or to have it produced internally.Internal production could use either of two processes. One would entail a variable cost of $17 perunit and an annual fixed cost of $200,000; the other would entail a variable cost of $14 per unitand an annual fixed cost of $240,000. Three vendors are willing to provide the part. Vendor A hasa price of $20 per unit for any volume up to 30,000 units. Vendor B has a price of $22 per unit fordemand of 1,000 units or less, and $18 per unit for larger quantities. Vendor C offers a price of $21per unit for the first 1,000 units, and $19 per unit for additional units.
a. If the manager anticipates an annual volume of 10,000 units, which alternative would be bestfrom a cost standpoint? For 20,000 units, which alternative would be best?
b. Determine the range for which each alternative is best. Are there any alternatives that are never best? Which?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! from 1 to 1000, vendor A is the cheapest.
this is because vendor A unit cost is 20 dollars while vendor B unit cost is 22 dollars and vendor C unit cost is 21 dollars.
internal option 1 and 2 are not considered because their minimum cost is 200,000 and 240,000 dollars respectively.
at 1000 units, vendor A, who is the cheapest of the vendors, has a total cost of 1000 * 20 = 20,000 dollars, which is well below the threshold of either of the internal options.
between 1001 and 59,999 units, vendor B is the cheapest.
this is because vendor B unit cost is 18 dollars while vendor A unit cost is still 20 dollars and vendor C unit cost is 19 dollars.
this continues until 60,000 units, at which time vendor B total cost and internal option 2 total cost are the same.
vendor B total cost is 60,000 * 18 = 1,080,000 dollars.
internal option 2 total cost is 240,000 + 14 * 60,000 = 1,080,000 dollars.
after 60,000 units, internal option 2 becomes, and stays, the cheapest.
Vendor C and internal option 1 are never the cheapest.
the break even point for the two internal options is determined as follows:
200,000 + 17x = 240,000 + 14x
subtract 14x from both sides and subtract 200,000 from both sides to get:
17x - 14x = 240,000 - 200,000
simplify to get 3x = 40,000
solve for x to get x - 13,333.33333333.....
13,334 units is when internal option 2 becomes cheaper than internal option 1.
at 13,334 units:
internal option 1 = 200,000 + 13,334 * 17 = 426,678
internal option 2 = 240,000 + 13,334 * 14 = 426,676
after 13,334 units, internal option 2 is the cheapest of the two.
at 13,334, the cheapest of the vendors, which is vendor B, total cost is 13,334 * 18 = 240,012.
vendor B continues to be the cheapest until 60,000 units, at which time vendor B and internal option 2 are tied at 1,080,000 dollars each.
after 60,000 units, internal option 2 takes over forever.
so, there you have it.
Vendor A cheapest to 1000 units.
vendor B cheapest from 1001 to 59,999 units.
vendor B and internal option 2 ties at 60,000 units.
internal option 2 cheapest from 60,001 units up.
vendor C and internal option 1 never the cheapest.
note that vendor A never gave an estimate for greater than 30,000 units.
in absence of any additional information on vendor A, i kept him at 20 dollars a unit.
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