A Small Store Is Trying to Determine If Its Current

question 22

Essay

A small store is trying to determine if its current checkout system is adequate. Currently, there is only one cashier, so it is a single-channel, single-phase system. The store has collected information on the interarrival time, and service time distributions. They are represented in the tables below. Use the following two-digit random numbers given below to simulate 10 customers through the checkout system. What is the average time in line, and average time in system? (Set first arrival time to the interarrival time generated by first random number.
$$\begin{array} { | c | c | c | c | c | } \hline \begin{array} { c } \text { Interarrival } \\\text { time (minutes) }\end{array} & \text { Probability } & & \begin{array} { c } \text { Service time } \\\text { (minutes) }\end{array} & \text { Probability } \\\hline 3 & .25 & & 1 & .30 \\\hline 4 & .25 & & 2 & .40 \\\hline 5 & .30 & & 3 & .20 \\\hline 6 & .20 & & 4 & .10 \\\hline\end{array}$$ Random numbers for interarrival times: 07, 60, 77, 49, 76, 95, 51, 16, 14, 85
Random numbers of service times: 57, 17, 36, 72, 85, 31, 44, 30, 26, 09

---

Definitions:

Time-Value

The principle stating that money in hand today is more valuable than the identical amount received later, owing to its capacity to generate earnings.

GDP Growth

The increase in the market value of goods and services produced by an economy over time, indicating economic health and progress.

Future Value

is the value of an asset at a specific date in the future, calculated from its present value and accounting for factors such as interest rates and time.

Present Value

The present-day worth of an anticipated future sum or series of cash payments, calculated using a specific interest rate.