Chapter 4, Problem 21RP

Explanation of Solution

• 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 $1,900 to a fire a worker.
• The overtime labor cost is:
  • 50$\left(\frac{15}{60}\right)$ = $12.5
• The material cost of a pair of shoes is $20
• The labor cost is:
• $\frac{2000}{150}\left(\frac{15}{60}\right)$= $3.33
• Therefore, the total production cost of a pair of shoes is:
  • 20+3.33=$23.33
• Therefore, the monthly cost of holding shoes in inventory is:
  • 23.33$\left(\frac{3}{100}\right)$ = $0