The Quality Sweaters Company sells hand-knitted sweaters. The company is planning to print a catalog of its products and undertake a direct mail campaign. The cost of printing the catalog is $20,000 plus $0.10 per catalog. The cost of mailing each catalog (including postage, order forms, and buying names from a mail-order database) is $0.15. In addition, the company plans to include direct reply envelopes in its mailings and incurs $0.20 in extra costs for each direct mail envelope used by a respondent. The average size of a customer order is $40, and the company’s variable cost per order (primarily due to labor and material costs) averages about 80% of the order’s value—that is, $32. The company plans to mail 100,000 catalogs. It wants to develop a spreadsheet model to answer the following questions: 1. How does a change in the response rate affect profit?2. For what response rate does the company break even?3. If the company estimates a response rate of 3%, should it proceed with the mailing?4. How does the presence of uncertainty affect the usefulness of the model?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter8: Evolutionary Solver: An Alternative Optimization Procedure
Section8.4: Nonlinear Pricing Models
Problem 5P
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The Quality Sweaters Company sells hand-knitted sweaters. The company is planning to print a catalog of its products and undertake a direct mail campaign. The cost of printing the catalog is $20,000 plus $0.10 per catalog. The cost of mailing each catalog (including postage, order forms, and buying names from a mail-order database) is $0.15. In addition, the company plans to include direct reply envelopes in its mailings and incurs $0.20 in extra costs for each direct mail envelope used by a respondent. The average size of a customer order is $40, and the company’s variable cost per order (primarily due to labor and material costs) averages about 80% of the order’s value—that is, $32. The company plans to mail 100,000 catalogs. It wants to develop a spreadsheet model to answer the following questions:

1. How does a change in the response rate affect profit?
2. For what response rate does the company break even?
3. If the company estimates a response rate of 3%, should it proceed with the mailing?
4. How does the presence of uncertainty affect the usefulness of the model?

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