BDA Tutorial 10

Tutorial 10: Monte Carlo Simulation I
Question 1:
For the past 50 days, daily sales of laundry detergent in a large grocery store have been
recorded (to the nearest 10).
Units Sold
30
40
50
60
70
Number of Times
8
12
15
10
5
a. Determine the relative frequency for each number of units sold.
b. Suppose that the following random numbers were obtained using Excel:
.12 .96 .53 .80 .95 .10 .40 .45 .77 .29
Use these random numbers to simulate 10 days of sales.
Question 2:
A pastry store wants to know how many dozen muffins to bake each day. Every dozen they
sell fresh in the shop returns a profit of \$5.00. Every dozen they bake but do not sell on the day
they are baked is given to a local charity at a loss of \$3.00 a dozen. The business is fairly stable
in that they never sell less than 50 dozen nor more than 80 dozen muffins. Their sales history,
rounded to the nearest ten dozen muffins is as shown:
Dozens of
Number of Days
Muffins Sold That many Sold
50
12
60
37
70
45
80
18
They want to run a ten day simulation for production rates of 50, 60, 70, and 80 muffins to
determine the profit (loss) for each. They generated the following random numbers for days
1‑10 respectively: .63, .13, .67, .50, .71, .25, .46, .00, .56, and .68.
a. Specify the random numbers range corresponding to each muffins-sold quantity.
b. Simulate 10 days of sales using four different daily production quantities: 50, 60, 70,
and 80 muffins per day. For each production quantity, compute the average daily profit.