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\title{Operations Research}
\author{Homework 11}
\date{Due in class Wednesday, December 7, 2016}
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\begin{enumerate}

\item \emph{(From HL, Exercise 19.3-4.)}  The Blue Cab Company is the
primary taxi company in the city of Maintown. It uses gasoline at the
rate of 8\,500 gallons per month. Because this is such a major cost,
the company has made a special arrangement with the Amicable Petroleum
Company to purchase a huge quantity of gasoline at a reduced price of
\$1.05 per gallon every few months. The cost of arranging for each
order, including placing the gasoline into storage, is \$1\,000. The
cost of holding the gasoline in storage is estimated to be \$0.01 per
gallon per month.

Use the EOQ model to find the optimal order quantity.

\item \emph{(HL, Exercise 19.3-14.)}
In the basic EOQ model, suppose the stock is replenished
uniformly (rather than instantaneously) at the rate of $b$ items per
unit time until the order quantity $Q$ is fulfilled. Withdrawals from
the inventory are made at the rate of $d$ items per unit time, where
$d<b$. Replenishments and withdrawals of the inventory are made
simultaneously. 

\begin{enumerate}
\item Find the total cost per unit time in terms of the setup cost
$K$, production quantity $Q$, unit cost $c$, holding cost $h$ per unit
per time, withdrawal rate $d$, and replenishment rate $b$.

\item Determine the economic order quantity $Q^*$.

\end{enumerate}
\end{enumerate}

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