Question 888529: Not sure if this will be too much but I need assistance with this problem.
What to do? (Hint: 200 x D is the same as 200D)
1. Option 1 - buy the part for 300 dollars per part.
2. Option 2 - purchase a machine that requires one operator (machine costs: 100,000 dollars and variable costs are 85 dollars per widget).
3. Option 3 - purchase a "no human needed machine" (machine costs: 250,000 dollars and variable costs are 30 dollars per widget).
Now then, find the breakeven point for "demand" (D) between options 1 and 2; 2 and 3. (Not you are not/not to find the breakeven point for "demand for 1 and 3).
Find the breakeven point like this:
a. For 1/2
Cost per part (times (I'll use the symbol * to represent times) (D) = Fixed costs + Variable Cost per part * (D)
Remember, you're solving for "D"
b. For 2/3
Fixed costs + Variable Cost per part * (D) (for option 2) = Fixed costs + Variable Cost per part * (D)
Remember, you're solving for "D"
c. If demand is 1,500 widgets, which option is best?
d. If demand is 3,000 widgets, which option is best?
e. If demand is 300 widgets, which option is best?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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