Let's consider the inventory problem with quantity discounts. The parameters are as follows: Annual demand lambda $=25000,$ Order cost K $=100,$ I $=0\mathrm{.}1.$ For order quantities between $0$ and $499,$ you pay c$($Q$)=21\mathrm{.}60$ per unit For order quantities between $500$ and $999,$ you pay c$($Q$)=20\mathrm{.}95$ per unit For order quantities $>=1000,$ you pay c$($Q$)=20\mathrm{.}90$ per unit. What is your total cost per year if your order quantity is $870$ per order?

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Let's consider the discrete demand newsvendor problem with the following parameters: Retail price $=45$ Purchase cost $=35$ Salvage value $=20$ Demand can assume values $\{0,1,2,3,4\}$ each with equal probability of p $=1/5.$ What is the expected overage cost if you order $1$ units?