Assuming that each products' sales value is proportional to the cost that is required to make it, then the percentage of total cost for each product should be:
Since this product collects 42% of the profits, it should approximately take 42% of the cost to produce.
42% of $100000 = $42,000 in costs for this product
If we sell the product for 50000 and pay 42000 in production cost then 8000 is the income
After further processing, we add 100000 to the 42000 to get 142000 in costs and it is sold for 190000 for an income of 48000.
The incremental income for this would then be 48000 - 8000 = 40000
In this case, the product should be PROCESSED FURTHER
8% of 100000 = 8000
You get 10000 off the product and have to pay approximately 8000 in costs for an income of 2000.
After further processing, you add 30000 in costs for 38000 and make 35000 for value to get an income of (3000)
The incremental income of this is (5000).
This product should be sold at SPLIT OFF
50% of 100000 = 50000
Sold at split off for 60000 for 10000 in income.
Add 150000 to process further for a total cost of 200000.
Sold after processing for 220000 for 20000 in income.
Incremental income is 10000.
Product should be PROCESSED FURTHER.
The new income is now 20000 + 48000 + 2000 = 70000
The reason why it is different than b is because you chose not to process further on product 14 and GAINED $5000 dollars more than processing them all.
I hope this is right... I haven't done this in awhile.