Answer:
Given,
Annual demand, D = 12500,
Setting up cost, S = $ 49,
Production rate per year, P = production facility × capability of production = 300 × 105 = 31500,
Holding cost per year, H = $ 0.15,
Hence,
(i) Optimal size of the production run,
![Q = \sqrt{\frac{2DS}{H(1-\frac{D}{P})}}=\sqrt{\frac{2\times 12500\times 49}{0.15(1-\frac{12500}{31500})}}=3679.60238126\approx 3680](https://tex.z-dn.net/?f=Q%20%3D%20%5Csqrt%7B%5Cfrac%7B2DS%7D%7BH%281-%5Cfrac%7BD%7D%7BP%7D%29%7D%7D%3D%5Csqrt%7B%5Cfrac%7B2%5Ctimes%2012500%5Ctimes%2049%7D%7B0.15%281-%5Cfrac%7B12500%7D%7B31500%7D%29%7D%7D%3D3679.60238126%5Capprox%203680)
(ii) Average holding cost per year,
![=\frac{QH}{2}(1-\frac{D}{P})](https://tex.z-dn.net/?f=%3D%5Cfrac%7BQH%7D%7B2%7D%281-%5Cfrac%7BD%7D%7BP%7D%29)
![=\frac{3680\times 0.15}{2}(1-\frac{12500}{31500})](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3680%5Ctimes%200.15%7D%7B2%7D%281-%5Cfrac%7B12500%7D%7B31500%7D%29)
![=166.476190476](https://tex.z-dn.net/?f=%3D166.476190476)
![\approx \$ 166.48](https://tex.z-dn.net/?f=%5Capprox%20%5C%24%20166.48)
(iii) Average setup cost per year,
![=\frac{D}{Q}\times S](https://tex.z-dn.net/?f=%3D%5Cfrac%7BD%7D%7BQ%7D%5Ctimes%20S)
![=\frac{12500}{3680}\times 49](https://tex.z-dn.net/?f=%3D%5Cfrac%7B12500%7D%7B3680%7D%5Ctimes%2049)
![=166.44021739](https://tex.z-dn.net/?f=%3D166.44021739)
![\approx \$ 166.44](https://tex.z-dn.net/?f=%5Capprox%20%5C%24%20166.44)
(iv) Total cost per year = average setup cost per year + average holding cost per year + cost to purchase 12500 lights
= 166.44 + 166.48 + 12500(0.95)
= $ 12207.92