Question 2 (35 pts): Joe Brown is the owner of Smiling Flowers shop in downtown

Question

Question 2 (35 pts): Joe Brown is the owner of Smiling Flowers shop in downtown Lincoln. Joe needs to decide on the number of roses to order from his supplier before the Valentine's Day. Joe buys each rose from the supplier at $4 per a rose and sells a rose at a price of $9 per rose. At this price, the anticipated demand is normally distributed with a mean of = 100 roses and a standard deviation of = 40 roses. Any leftover rose at the end of Valentine's Day will be sold at a discounted price of $1 per rose Assume that each customer demands one rose Note: The questions in sections (a) to (e) below are independent. That is, in each section use the information given above unless otherwise is stated in that specific section. For instance, in section (b) demand information is given as uniform distribution. In this section use this uniform distribution info However in the remaining sections, use the demand information of normal distribution as given in the original question above. demand infor a) (7 pts): Given the information above, how many roses should Joe order before the Valentine's Day? b) (7 pts): If the anticipated demand had a uniform distribution between 100 and 200, how many roses would Joe order before the Valentine's Day? c) (7 pts): Suppose a customer who is unable to purchase a rose (due to stock out at Smiling Flowers) settles for buying a daisy bouquet. A bouquet sells for $10 and costs Smiling Flowers $8 each. Smiling Flowers never runs out of bouquets. In this case, how many roses would Joe Brown order before the Valentine's Day? d) (7 pts): Suppose it costs $1 to hold a rose in the inventory for the selling season. This holding cost is incurred only for the roses that are not sold by the end of Valentine's Day. In this case, how many roses would Joe Brown order before the Valentine's Day? e) (7 pts): If Joe Brown orders 180 roses at the beginning of the selling season, what is the probability that Smiling Flowers will sell all the roses by the end of Valentine's Day?

Explanation / Answer

(a)

Cu = Cost of underage = Selling price - cost = $9 - $4 = $5
Co = Cost of overage = Cost - salvage value = $4 - $1 = $3

Critical ratio = Cu / (Co+Cu) = 5 / 8 = 0.625

At this cumulative probability, the value of standard normal variable is Z = NORMSINV(0.625) = 0.319

Optimal Order Size = Mean Demand + Z x SD = 100 + 0.319 x 40 = 113 roses.

(b)

In this case, the order size would be Q = 0.625 x (200 - 100) + 100 = 163 roses

(c)

Cu = $5 - Recovery by bouquet = $5 - ($10 - $8) = $3
Co = same as part (a) = $3

Critical ratio = Cu / (Co+Cu) = 3 / 6 = 0.50

At this cumulative probability, the value of standard normal variable is Z = NORMSINV(0.5) = 0

Optimal Order Size = Mean Demand + Z x SD = 100 roses.

(d)

Cu = Cost of underage = Selling price - cost = $9 - $4 = $5
Co = Cost of overage = Cost - salvage value + carrying cost = $4 - $1 + $1 = $4

Critical ratio = Cu / (Co+Cu) = 5 / 9 = 0.555

At this cumulative probability, the value of standard normal variable is Z = NORMSINV(0.555) = 0.140

Optimal Order Size = Mean Demand + Z x SD = 100 + 0.140 x 40 = 106 roses.

(e)

Prob(Demand >= 180) = 1 - NORMDIST(180,100,40,TRUE) = 0.02275

So, All the flowers will be sold has probability = 0.02275

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.