Question 888529
let x equal the number of widgets.


option 1 cost = 300 * x


option 2 cost = 100,000 + 85 * x


breakeven point is when these costs are equal to each other.


300 * x = 100,000 + 85 * x


solve for x to get x = 465.1162791...


cost for option 1 becomes 300 * 465.1162791... = 139,534.8837...


cost for option 2 becomes 100,000 + 85 * 465.1162791 = 139,534.8837...


cost for option 1 and option 2 is equivalent when the number of widgets is equal to 465.1162791...


option 2 cost is 100,000 + 85 * x


option 3 cost is 250,000 + 30 * x


these 2 options break even when the cost for option 2 is the same as the cost for option 3.


set these costs equal to each other and solve for x.


100,000 + 85 * x = 250,000 + 30 * x


solve for x to get x = 2727.2727...


cost for option 2 becomes 100,000 + 85 * 2727.2727... = 331,818.1818...


cost for option 3 becomes 250,000 + 30 * 2727.2727... = 331,818.1818...


cost for option 2 and 3 are equivalent when the number of widgets is equal to 2727.2727...


if demand is 1500 widgets, these are the costs:


option 1 = 300 * 1500 = 450,000
option 2 = 100,000 + 85 * 1500 = 227,500 
option 3 = 250,000 + 30 * 1500 = 295,000


the least cost option at 1500 widgets is option 2.


if the demand is 3000 widgets, these are the costs:


option 1 = 300 * 3000 = 900,000
option 2 = 100,000 + 85 * 3000 = 355,000
option 3 = 250,000 + 30 * 3000 = 340,000


the least cost option at 3000 widgets is option 3.


if the demand is 300 widgets, these are the costs:


option 1 = 300 * 300 = 90,000
option 2 and option 3 are both greater than 100,000 because of their fixed costs.


the least cost option at 300 widgets is option 1.