4. (15 PTS) The IIE student chapter plans to sell T-shirts to raise money for th

Question

4. (15 PTS) The IIE student chapter plans to sell T-shirts to raise money for the regional conference. Demand for the T-shirts is thought to be uniformly distributed from 50-100. Each T-shirt costs $9.00 and will be sold for $17.00. The IIE student chapter officers believe shirts left over after the conference can be sold for $5.00. The order can only be placed once. a. How many T-shirts should be ordered? b. What is the expected number of unsold shirts if the number calculated in part a is ordered? c. What is the expected number of shirts that will be short if the number in part a is ordered? d. What is the expected profit from this fund raising activity?

Explanation / Answer

Ansss
Shortage or Underage cost, Cu = lost opportunity of earning profit by selling 1 less unit than demand = 17-9 = $ 8
Excess or Overage cost Co = Loss suffered by ordering 1 extra unit than demand = 9 - 5 = $ 4
Critical ratio CR = Cu / (Cu + Co) = 8 / (8+4) = 0.67
Optimal number of shirts to be ordered = 50 + 0.67*(100-50) = 83
Expected Shortage = = 1/(250-50)*(D2/2 - 83D|D=250D=83 = 1/200* {(2502/2 - 83*250) - (832/2 - 83*83)} = 70
Where f(D) is the pdf of Demand. f(D) = 1 / (250-50)
Expected Sales = Average Demand - Expected shortage = 150 - 70 = 80
Expected number of unsold shirts = Quantity ordered - Expected sales = 83 - 80 = 3
Expected Profit = Expected sales*underage cost - leftover inventory*overage cost = 80*8 - 3*4 = $ 628
Answer Summary
a) T-shirts should be ordered = 83
b) Expected number of unsold shirts if the number calculated in part a is ordered = 3
c) Expected number of shirts that will be short if the number in part a is ordered = 70
d) Expected profit from this fund raising activity = $ 628

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

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