IM.54 A growing online retailer sells thousands of items yet has has one specialty product category with just 30 items. They want to classify these thirty items according to the annual dollar volume (revenue) generated by each item. The table below lists each item number, Annual Sales (in units), and Price per unit: Item # Annual Sales Price 1 221 $25.85 2 446 $14.15 3 8,940 $168.19 4 2,965 $15.99 5 1,322 $29.37 6 2,575 $12.77 7 767 $28.43 8 5,803 $163.01 9 2,673 $20.51 10 642 $14.71 11 4,168 $54.53 12 1,881 $22.55 13 2,417 $29.63 14 5,207 $36.41 15 1,381 $20.55 16 9,635 $173.69 17 17,406 $27.07 18 1,573 $25.99 19 6,471 $64.99 20 6,047 $29.83 21 433 $20.89 22 2,279 $53.59 23 15,532 $106.91 24 1,585 $4.09 25 5,376 $65.23 26 2,965 $37.93 27 2,048 $28.51 28 1,174 $22.99 29 381 $5.57 30 2,930 $3.43 Which item in the table above has the highest annual dollar volume? In the answer field below, write the ITEM # that corresponds to your answer. Do not put a period after the number. What is the annual dollar volume for the item you selected in the previous question? (Display your answer to the nearest whole number.) Suppose that the "A" items constitute up to 70 percent of the annual dollar volume of all the parts in the list. How many "A" items should there be? Suppose the "B" items are for the next 20 percent of annual dollar volume and that the "C" items are for the remaining 10 percent of annual dollar volume. How many "C" items should there be?

IM.54 A growing online retailer sells thousands of items yet has has one specialty product category with just 30 items. They want to classify these thirty items according to the annual dollar volume (revenue) generated by each item. The table below lists each item number, Annual Sales (in units), and Price per unit: Item # Annual Sales Price 1 221 $25.85 2 446 $14.15 3 8,940 $168.19 4 2,965 $15.99 5 1,322 $29.37 6 2,575 $12.77 7 767 $28.43 8 5,803 $163.01 9 2,673 $20.51 10 642 $14.71 11 4,168 $54.53 12 1,881 $22.55 13 2,417 $29.63 14 5,207 $36.41 15 1,381 $20.55 16 9,635 $173.69 17 17,406 $27.07 18 1,573 $25.99 19 6,471 $64.99 20 6,047 $29.83 21 433 $20.89 22 2,279 $53.59 23 15,532 $106.91 24 1,585 $4.09 25 5,376 $65.23 26 2,965 $37.93 27 2,048 $28.51 28 1,174 $22.99 29 381 $5.57 30 2,930 $3.43 Which item in the table above has the highest annual dollar volume? In the answer field below, write the ITEM # that corresponds to your answer. Do not put a period after the number. What is the annual dollar volume for the item you selected in the previous question? (Display your answer to the nearest whole number.) Suppose that the "A" items constitute up to 70 percent of the annual dollar volume of all the parts in the list. How many "A" items should there be? Suppose the "B" items are for the next 20 percent of annual dollar volume and that the "C" items are for the remaining 10 percent of annual dollar volume. How many "C" items should there be?

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 56P

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IM.54 A growing online retailer sells thousands of items yet has has one specialty product category with just 30 items. They want to classify these thirty items according to the annual dollar volume (revenue) generated by each item. The table below lists each item number, Annual Sales (in units), and Price per unit:

Item #	Annual Sales	Price
1	221	$25.85
2	446	$14.15
3	8,940	$168.19
4	2,965	$15.99
5	1,322	$29.37
6	2,575	$12.77
7	767	$28.43
8	5,803	$163.01
9	2,673	$20.51
10	642	$14.71
11	4,168	$54.53
12	1,881	$22.55
13	2,417	$29.63
14	5,207	$36.41
15	1,381	$20.55
16	9,635	$173.69
17	17,406	$27.07
18	1,573	$25.99
19	6,471	$64.99
20	6,047	$29.83
21	433	$20.89
22	2,279	$53.59
23	15,532	$106.91
24	1,585	$4.09
25	5,376	$65.23
26	2,965	$37.93
27	2,048	$28.51
28	1,174	$22.99
29	381	$5.57
30	2,930	$3.43

Which item in the table above has the highest annual dollar volume? In the answer field below, write the ITEM # that corresponds to your answer. Do not put a period after the number.

What is the annual dollar volume for the item you selected in the previous question? (Display your answer to the nearest whole number.)

Suppose that the "A" items constitute up to 70 percent of the annual dollar volume of all the parts in the list. How many "A" items should there be?

Suppose the "B" items are for the next 20 percent of annual dollar volume and that the "C" items are for the remaining 10 percent of annual dollar volume. How many "C" items should there be?

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Scenario 3 Ben Gibson, the purchasing manager at Coastal Products, was reviewing purchasing expenditures for packaging materials with Jeff Joyner. Ben was particularly disturbed about the amount spent on corrugated boxes purchased from Southeastern Corrugated. Ben said, I dont like the salesman from that company. He comes around here acting like he owns the place. He loves to tell us about his fancy car, house, and vacations. It seems to me he must be making too much money off of us! Jeff responded that he heard Southeastern Corrugated was going to ask for a price increase to cover the rising costs of raw material paper stock. Jeff further stated that Southeastern would probably ask for more than what was justified simply from rising paper stock costs. After the meeting, Ben decided he had heard enough. After all, he prided himself on being a results-oriented manager. There was no way he was going to allow that salesman to keep taking advantage of Coastal Products. Ben called Jeff and told him it was time to rebid the corrugated contract before Southeastern came in with a price increase request. Who did Jeff know that might be interested in the business? Jeff replied he had several companies in mind to include in the bidding process. These companies would surely come in at a lower price, partly because they used lower-grade boxes that would probably work well enough in Coastal Products process. Jeff also explained that these suppliers were not serious contenders for the business. Their purpose was to create competition with the bids. Ben told Jeff to make sure that Southeastern was well aware that these new suppliers were bidding on the contract. He also said to make sure the suppliers knew that price was going to be the determining factor in this quote, because he considered corrugated boxes to be a standard industry item. As the Marketing Manager for Southeastern Corrugated, what would you do upon receiving the request for quotation from Coastal Products?
Pricing Decisions at Madison The Madison Company manufactures and retails a certain product. The company wants to determine the price that maximizes its profit from this product. The unit cost of producing and marketing the product is 50. Madison will certainly charge at least 50 for the product to ensure that it makes some profit. However, there is a very competitive market for this product, so that Madisons demand falls sharply when it increases its price. How should the company proceed?2 In the pricing model in Example 7.1 with the constant elasticity demand function, the assumption is that all units demanded are sold. Suppose the company has the capacity to produce only 200 units. If demand is less than capacity, all of demand is sold. If demand is greater than or equal to capacity, only 200 units are sold. Use Solver to find the optimal price and the corresponding profit. Then use SolverTable to see how sensitive these answers are to the production capacity, letting it vary from 170 to 230 in increments of 10. Discuss your findings relative to the original solution in Example 7.1. In other words, what is the effect of capacity on the optimal price and profit?

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