Question

Clio’s Floral Shoppe buys roses each week from Panama. Orders are placed online on Saturday night, and early Monday morning roses arrive at the airport in a box refrigerated with dry ice. The roses cost $8 a dozen and are sold on a cash-and-carry basis for $28 a dozen. Roses left over at the end of the week are put in a trash collector in an alley behind the store. Past sales (rounded to the nearest ten dozen) are as follows

Dozens of Roses          Relative

    Demanded            Frequency

         110                       5

         120                         20

         130                         25

         140                         30

         150                         20

​The owner of Clio’s Floral Shoppe wants to compare two ordering rules for ordering roses: (1) order last week’s demand plus 10 dozen extra (as safety stock), (2) order 125 dozen every week. She wants to run a ten-week simulation to compare the average weekly profit for the two rules. Last week's demand was for 110 dozen.

Simulate ten weeks of operation using each of the ordering rules and compute the average weekly profit resulting from each rule.In your simulation, use the following random numbers to generate rose demand in weeks 1‑10, respectively:

0.28962936
0.68126264
0.41410883
0.26505633
0.48749513
0.28695576
0.8450472
0.14285232
0.96957178
0.05764064

​

1. What is the average profit if she orders using rule 1?

2. What is the average profit if she orders using rule 2?

Answer 1

Solution

Preparatory Work

Let the actual (or simulated) demand be D.

Profit per dozen sold = sales value – cost = 28 – 8 = 20

Loss per dozen not sold = cost per dozen =

Then, weekly profit unde the two ordering rules would be:

Rule 1:

If D ≥ 110, only 110 dozens will be sold. So, the net profit would be: (110 x 20) = 2200 ………(1a)

If D < 110, only D dozens will be sold and (110 - D) will be unsold. So, the net profit would be:      (D x 20) - 8(110 - D) = 28D - 880 ……………………………………………...................…(1b)

Rule 2:

If D ≥ 130, only 130 dozens will be sold. So, the net profit would be: (130 x 20) = 2600 ………(2a)

If D < 130, only D dozens will be sold and (130 - D) will be unsold. So, the net profit would be:

(D x 20) - 8(130 - D) = 28D - 1040