A doohickey producer wants to find the minimum cost necessary to manufacture doo

Question

A doohickey producer wants to find the minimum cost necessary to manufacture doohickeys. The manufacturer expects to make 5600 doohickeys at a steady rate during the next year. Production runs of the same number of doohickeys will be evenly spaced throughout the year. The cost for each production run is $175. Carrying costs, based on the average number of doohickeys in stock, amount to $1 per doohickey. Let x be the number of doohickeys made per production run and r be the number of production runs during the year.

Determine the number of production runs per year and the number of doohickeys per production run that minimize cost: runs and doohickeys.
The minimal production cost is $ .

Explanation / Answer

Expected number of sale : 5600
That means r*x= 5600

r=5600/x --- (1)

Production run cost = 175*r =175*5600/x

Average inventory = (x) /2 = x/2

Inventory carrying cost = x/2

Total cost = Production run cost + inventory carrying cost

C = 980000/x+ x/2

To calculate optimum :

dC/dx = -980000/x^2 + 1/2 =0

x^2 = 1960000

x= 1400

Then r=5600/1400 = 4

Minimum cost : 980000/1400+1400/2 = $1400

All the answers in the sequence below :

1) Number of Production run (r) = 4

2) number of doohickeys made per production run (x) = 1400

3) Minimum cost = $1400

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