# Math Help - Need Help-Cost analysis got me going crazy

1. ## Need Help-Cost analysis got me going crazy

So i have two options with a product
Product X
Cost-1.10
Startup-600

Product Y
Cost 1.05
Startup 2500

i want to know how many of product Y i have to buy before the lower cost outweighs the higher startup 

Here is what i have come up with so far

Cost = 2500+1.05X
Cost = 600+1.10X

Maybe substitution method but i cannot figure out my two initial equations to start with.

i know i can plug in numbers all day to figure out the value, but the fact that i cannot come up with the true math formula will drive me crazy all weekend. Any help would be appreciated

2. Option A, product x:
Cost per unit = $1.10 Initial Cost =$600
Total cost = 1.10x + 600

Option B, product x:
Cost per unit = $1.05 Initial Cost =$2500
Total cost = 1.05x + 2500

Now, what you are looking for is the number of units of product x where economies of scale begins to pay off. To do this, find the number of units for when the cost of Options A & B are equal.

1.10x + 600 = 1.05x +2500
.05x = 1900
x = 38000

When you are producing 38000 units, you will be indifferent to the two options because each costs the same. This can also be found by graphing the lines and finding their intersection, but it might be a pain to set the window right (ie: TI-83).

The other thing to look for is when to use which option. Assume you produce 0 units. Option A will be cheaper. This means that if you are producing 0 to 38000, you should use option A. Of course, this also means that if you are producing 38000 or more, option B should be used.