Answer:
the optimal order size Q is 18.56 cars
the annual inventory cost = $12066.48
the order cycle time is 42.34 days
Explanation:
Using the following expression to determine the optimal order size Q:
[tex]Q = \sqrt{\frac{2* ordering \ cost \ * Demand}{Annual \ carrying \ cost }}[/tex]
[tex]Q = \sqrt{\frac{2* 700 * 160}{650 }}[/tex]
[tex]Q =\sqrt{344.6153846}[/tex]
[tex]Q = 18.56[/tex]
Hence; the optimal order size Q is 18.56 cars
The annual inventory cost is mathematically expressed as:
[tex]\frac{ordering \ cost * Demand}{optimal \ order \ size} + \frac{annual \ carrying \ cost}{2}[/tex]
= [tex]\frac{700*160}{18.56} +\frac{650*18.56}{2}[/tex]
= 6034.482759 + 6032
= $12066.48276
≅ $12066.48
Hence, the annual inventory cost = $12066.48
For The order cycle time; we have;
Order cycle time = [tex]\frac{365 \ days }{1} \div ( \frac{ Demand }{optimal \ order \ time })[/tex]
= [tex]\frac{365 }{1} \div (\frac{160 }{18.56})[/tex]
= [tex]\frac{365 }{1} \div (8.62)[/tex]
= [tex]\frac{365 }{1} \times \frac{1}{ 8.62}[/tex]
= 42.34 days
Hence, the order cycle time is 42.34 days
