Price and Probability Calculation on Producing Items

64 Views Asked by At

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.

1

There are 1 best solutions below

0
On

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"?)