Problem $20-39($Algo$)$

$\backslash ($ C U $\backslash ),$ Incorporated $($CUI$),$ produces copper contacts that it uses in switches and relays. CUI needs to determine the order quantity, $\backslash ($ Q $\backslash ),$ to meet the annual demand at the lowest cost. The price of copper depends on the quantity ordered. Here are price$-$break and other data for the problem:

Price of copper $\backslash (\backslash$$ $0\mathrm{.}81\backslash )$ per pound up to $2,499$ pounds

$\backslash (\backslash$$ $0\mathrm{.}80\backslash )$ per pound for orders between $2,500$ and $4,999$ pounds

$\backslash (\backslash$$ $0\mathrm{.}78\backslash )$ per pound for orders $5,000$ pounds or greater

Annual demand $\backslash (\backslash$quad $51,000\backslash )$ pounds per year

Holding cost $\backslash (\backslash$quad $30\backslash )$ percent per unit per year of the price of the copper

Ordering cost $\backslash$$ $30$

Which quantity should be ordered?

Quantity