Consider the simple inventory problem for an assembly part utilized in a production facility. The daily demand $D$ is an exponentially distributed random variable with a mean of $10$ units per day $(=0\mathrm{.}1).$ Parts are ordered in a batch of $Q$ units. The total inventory cost $($TC$)$ per day is given by the equation as a function of holding and ordering costs as follows:

$TC=(C_h\frac{Q}{2})+(\frac{C_{aD}}{Q}),or,TC=(0\mathrm{.}1**\frac{Q}{2})+(12\mathrm{.}5**\frac{D}{Q})$

based on a holding cost of $C_h=0\mathrm{.}1$$ $/$unit per day and an ordering cost of $C_0=12\mathrm{.}5$$ $/$order as seen in the equation above. It is required to determine the best order quantity, which is a decision variable. Simulate this system for $5$ consecutive days to determine average total inventory cost for the order quantities of $Q=40,Q=50$ and $Q=60$ units and indicate the best order quantity. Use the second row of uniform random numbers table below to generate the random demand $($starting from $0\mathrm{.}180$ as given$)$ for your $($you may use the same random numbers for evaluating $Q=40,Q=50$ and $Q=60).$ Use the table below.

a$)$ Determine the best order quantity based on your results. Use two digits accuracy.

$\backslash$table$[[U_i,D_i,\backslash$table$[[$TC for$],[Q=40$