I'm hoping someone can help me out here.
Product A can be produced from Product B at a 50% chance.
Product B can be produced from Product D at a 25% chance and a cost of \$1400 success, and \$700 for a fail.
The goal is to produce 5 x Product A.
Does anyone know how I could predict the cost of producing 5 x Product A? And at what price if Purchasing Product D would be cheaper to purchase than produce it?
I'm thinking it'll cost \$3,500 to get Product B (3 fails, 1 success). Then \$7,000 to get Product A (1 fail, 1 success).
So repeating to obtain 5 x Product A, it will be at a cost of \$35,000. Less than \$3,500 is the price I should look to get Product B rather than produce it.
Suppose we start with 1000 (chosen because it is an easy number to work with) of "product D". We try to convert that to "product B". 25% of the time, so 250 times we get "product B", 750 times we fail. That costs 250(\$1400)+ 750(\$700)= \$875,000. Half of the "product B", 125 times, we get "product A". Nothing is said about "cost" converting form "B" to "A" so the cost of producing 125 of A is still \$875,000.
Since the question asked about 5, rather than 125, divide every thing by 25:
Starting with 1000/25= 40 of "product D" we produce 250/25= 10 of "product B" at a cost of \$875,000/25= \$35,000. From those we produce 125/25= 5 of "product A".
(What happened to "product C"?)