Answer: Q = 6,440
Explanation:
Annual demand = D = 12,200
Setting up cost = O = $51
Production rate per year = P = Operating days × Producing capability
= 300 days a year × 100 per day
= 30,000
Holding cost per year = H = $0.05 per light
[tex]X = \frac{D}{P}[/tex]
[tex]X = \frac{12,200}{30,000}[/tex]
= 0.4
Therefore,
Optimal size of the production run, Q
[tex]=\sqrt{\frac{2OD}{H(1-x)} }[/tex]
[tex]=\sqrt{\frac{2\times51\times12,200}{0.05(1-0.4)}}[/tex]
[tex]=\sqrt{\frac{1,244,400}{0.03}}[/tex]
[tex]=\sqrt{41,480,000}[/tex]
= 6,440.49
Q = 6,440