Respuesta :
Answer:(a.) Economic batch size = 1,414 units
(b.) Maximum inventory level = 530 units
(c.) Number of order cycles = 8.84 cycles per year
(d.) Total annual holding and setup costs = $2,651
Explanation:
Given:
Annual demand (D) = 12,500 units
Setup cost (S) = $150
Holding cost (H) = $5 per unit per year
Daily production (p) = 80 units per day
Daily Demand (d) = 50 units per day
(a) Economic batch size (Q):
Q = [tex]\sqrt{\frac{[(2 \times D \times S)]}{H \times (1 - \frac{d}{p} )} }[/tex]
Q = [tex]\sqrt{\frac{[(2 \times 12500 \times 150)]}{5 \times (1 - \frac{50}{80} )} }[/tex]
Q = 1,414.21 [tex]\simeq[/tex] 1,414
Economic batch size = 1,414 units
(b) Maximum inventory level ([tex]I_{max}[/tex]):
[tex]I_{max}[/tex] = Q × (1 - [tex]\frac{d}{p}[/tex])
[tex]I_{max}[/tex] = 1,414 × (1 - [tex]\frac{50}{80}[/tex])
[tex]I_{max}[/tex] = 530.25 [tex]\simeq[/tex] 530
Maximum inventory level = 530 units
(c) Number of order cycles:
Number of order cycles = [tex]\frac{D}{Q}[/tex]
Number of order cycles = [tex]\frac{12500}{1414}[/tex]
Number of order cycles = 8.84 cycles per year
(d) Total annual holding and setup costs:
Total costs = Annual holding + Annual setup costs
Total costs = [([tex]I_{max}[/tex] ÷ 2) × H] + [Number of order cycles × S]
Total costs = [(530 / 2) × $5] + [8.84 × $150]
Total costs = $1,325 + $1,326
Total costs = $2,651
