Answer:
The manufacturer have to produce 20,000 circuit boards per run with 50 production runs
Explanation:
Let x = number of circuit boards to be produced
An average of x/2 circuit boards are stored throughout the year at a cost of $2 each;
so annual storage cost = x/2*2 = x
Note: it costs $10 each to produce x circuit boards and $400 to set up
Therefore, The cost per run = 10x + 400
The 1,000,000 circuit boards at x circuit board per run would require 1000000/x runs.
Therefore, production costs = cost per run * production run
production costs = (10x + 400)*(1000000/x) = 10,000,000 + 400,000,000/x
Total cost C = storage cost + production cost
C = x + 10,000,000 + 400,000,000/x
Set c to zero and differentiate c with respect to x
0=1+0-400,000,000/x²
Therefore x = 20,000
Number of circuit boards that should be produced to minimize cost is 20,000
While the production runs needed = 1,000,000/x = 1,000,000/20,000= 50
The manufacturer have to produce 20,000 circuit boards per run with 50 production runs
