Answer:
16,000 units.
Step-by-step explanation:
The classic model for inventory involves:
K=set up cost per order. In this case, $640
D=demand. In this case, 150,000 units.
h=holding cost per unit per year. In this case, $0.75 each
[tex]\text{Total Cost per Unit Time, TCU} = \displaystyle \frac{K}{\frac{y}{D}}+h(\frac{y}{2})[/tex]
The optimum order is found by minimizing TCU.
[tex]\displaystyle \frac{d(TCU(y))}{dy}=\frac{-KD}{y^{2}}+\frac{h}{2}=0[/tex]
[tex]\displaystyle y=\sqrt{\frac{2KD}{h}}=\sqrt{\frac{2(640)(150000)}{0.75}}=16,000[/tex]
The number of items that should be produced in each run so that total costs of production and storage are minimized is 16,000 units.
