Geoff Gullo owns a small firm that manufactures “Gullo Sunglasses”. This season’

Question

Geoff Gullo owns a small firm that manufactures “Gullo Sunglasses”. This season’s demand for this model will be normally distributed with mean 200 and standard deviation 100. Land’s Start will sell those sunglasses for $96 each. Geoff’s unit production cost is $30. He has the opportunity to sell a particular seasonal model to Land’s Start, a catalog retailer. Geoff offers Land’s Start two purchasing options. Option 1: Geoff offers to set his price at $67 and agrees to credit Land’s Start $51 for each unit Land’s Start returns to Geoff at the end of the season (because those units did not sell). Since styles change each year, there is essentially no value in the returned merchandise. Option 2: Geoff offers a price of $57 for each unit, but returns are no longer accepted. In this case Land’s Start throws out unsold units at the end of the season. If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method. a. How much would Land’s Start buy if they chose option 1? Use Table 13.4 and round-up rule. (Round your answer up to a whole number.) b. How much would Land’s Start buy if they chose option 2? Use Table 13.4 and round-up rule. (Round your answer up to a whole number.) c. Use Table 13.4. Which option will Land’s Start choose? Complete the table on the right: Option 1 Option 2 (Round your answer to 2 decimal places.) Expected Inventory Expected sales Expected profit d. Suppose Land’s Start chooses option 1 and orders 250 units. What is Geoff Gullo’s expected profit? Use Table 13.4. Do not round intermediate calculations. (Round your answer up to a whole number.) 20 6-9-3-8-4-1-8 2 4-5-6-7-8-9 3-4 2|2|2|2|2|2|3|3|3|3|3|3|3|3|3|3|4 .. 2 0 9-9-9-9-9-9-9 7-7. | 8 | 8 | 8 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 9|9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9 1-7|2|6|9|1|3|5-6-7-8-8 1-1 .4 5 | 6 | 7 | 8 | 9 | 0 1 | 2 | 3 | 4 5 6 7 8 | 9|01|234567890 .. th 2-9-7-8 0-2-8-7 2-4-6-9-3-6 3-6-1-5 3-8-6-5. 8-6-5-4 1 7-8-2-0 6-3-9-6-4-2 5-6-6-7-8-9 2 5-7|0|1|9|3|3|9-2. 6-5-5-8|4|1|2|4|8 4|2|0 1|3|5|8|1|4|7-0-4-8-2 3 .2 1 | O 3 8 7 6 5 4 | 3 | 2 | 1 | 0 1 | 2 3 4 5 6 7 | 8 | 9|01|23 .. I-la 5-8|1|5|0|7-7-9-5-5|1|3|3|2|3|7 .. 8-1-4-8|3|9-64 1-1-2-2-3 1|1|2|2|3|5|7|0|3|9-6-5|7|2|2|7-9-9-8-7-9-6-8-8-8 1-1-2-3 .O 9 | 8 7 6 5 4 3 2 | 1 | 0 | 9 | 8 | 7 | 6 | 5 4 3 2 1 0 | 9 | 8 7 6 54.

Explanation / Answer

a) Option 1

For Land's Start, Underage cost, Cu = selling price - purchase price = 96 - 67 = 29

Overage cost, Co = Cost - Salvage = 67 - 51 = 16

Critical ratio, F(z) = Cu(Cu+Co) = 29/(29+16) = 0.6444

Using Table 13.4, z = 0.4 (using round-up rule)

Optimal quantity Land's Start should buy, Q = m + z*s = 200 + 0.4*100 = 240

____________________________________________

b) Option 2

For Land's Start, Underage cost, Cu = selling price - purchase price = 96 - 57 = 39

Overage cost, Co = Cost - Salvage = 57

Critical ratio, F(z) = Cu(Cu+Co) = 39/(39+57) = 0.4063

Using Table 13.4, z = -0.2 (using round-up rule)

Optimal quantity Land's Start should buy, Q = m + z*s = 200 - 0.2*100 = 180

____________________________________________

c)

Option 1, z = (240-200)/100 = 0.4

I(z) = 0.6304

Expected Inventory, V = s*I(z) = 100*0.6304 = 63.04

Expected Sales, S = Q - V = 240 - 63.04 = 176.96

Expected Profit = S*Cu - V*Co = 176.96*29 - 63.04*16 = $ 4123.20

__________________

Option 2, z = (180-200)/100 = -0.2

I(z) = 0.3069

Expected Inventory, V = s*I(z) = 100*0.3069 = 30.69

Expected Sales, S = Q - V = 180 - 30.69 = 149.31

Expected Profit = S*Cu - V*Co = 149.31*39 - 30.69*57 = $ 4073.76

____________________________________________

d) Q = 250

Option 1, z = (250-200)/100 = 0.5

I(z) = 0.6978

Expected Inventory, V = s*I(z) = 100*0.6978 = 69/78

Expected Sales, S = Q - V = 250 - 69.78 = 180.22

Expected Profit = S*Cu - V*Co = 180.22*29 - 69.78*16 = $ 4109.90

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

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