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Calyna eximionsdr

testor $\frac{1}{2}$

Q$3$: A manufacturer of plastic bottles needs $1500$ kg of raw material each year and sources it from its supplier. Every time the manufacturer places an order, it incurs a cost of $$20.$ The carrying cost rate is $25\%$ per year. The purchasing price of raw material is based on the size of the order as shown below:

Cost per kg

Cost per $kg=\{\begin{array}{ccc}\text{\$}1\mathrm{.}00,& \text{f}\text{o}\text{r}\text{o}\text{r}\text{d}\text{e}\text{r}\text{s}\text{i}\text{z}\text{e}\text{b}\text{e}\text{t}\text{w}\text{e}\text{e}\text{n}0\text{a}\text{n}\text{d}& 499kg\\ \text{\$}0\mathrm{.}99,& \text{f}\text{o}\text{r}\text{o}\text{r}\text{d}\text{e}\text{r}\text{s}\text{i}\text{z}\text{e}\text{b}\text{e}\text{t}\text{w}\text{e}\text{e}\text{n}500\text{a}\text{n}\text{d}& 999kg\\ \text{\$}0\mathrm{.}98,& \text{f}\text{o}\text{r}\text{o}\text{r}\text{d}\text{e}\text{r}\text{s}\text{i}\text{z}\text{e}\text{a}\text{b}\text{o}\text{v}\text{e}& 1000kg\end{array}$

Assuming all$-$units discount, determine the feasible and optimal order quantity.