Question 1118030
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.