Suppose that,

w_t = Number of shoemakers in the workforce during month t.

h_t = Number of shoemakers hired at the beginning of the month t.

f_t = Number of shoemakers fired at the beginning of the month t.

r_t = Pair of shoes produce during regular time in month t.

o_t = Pair of shoes produce during overtime in month t.

i_t = Pair of shoes in the inventory at the end of month t.

z = Cost of the company

The regular salary of a shoemaker is $2,000 per month and it costs $1,500 to hire a worker and $1,900 to a fire a worker.

The overtime labor cost is:

50(1560) = $12.5

The material cost of a pair of shoes is $20

The labor cost is:

2000150(1560)= $3.33

Therefore, the total production cost of a pair of shoes is:

20+3.33=$23.33

Therefore, the monthly cost of holding shoes in inventory is:

23.33(3100) = $0

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Chapter 4, Problem 20RP

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