Math 251
Project 1 Assignment
Final report due : 10/5
You are to act as consultants to Electronic Communications for the project described here.
Your job is to determine the best allocation strategy, including the allocations of personnel time and advertising expenditures to the different sales/distribution channels. You need to provide as much advice as possible regarding the effects of changes in conditions - in particular answering the question that have already been raised [given below].
Your results should be written up as a formal report (paragraph form, typed, with page numbers, tables/figures/graphs [if appropriate], but no calculations, formulas or technical mathematical terms) of two or three pages length. Your text includes some nice models of formal reports on pp30-32, pp80-81, pp.162-166 – you don’t have to follow these outlines, but the basic style should be similar [assume the readers haven’t a clue about linear programming, and don’t expect to learn].
Supporting formulas, model definitions, any relevant computer printout (presumably all calculations are done with computer software) should be included in a technical appendix attached to the report. This should include the formal linear programming setup of the problem (including definition of variables, identification of objective, etc.)
With the report, please include a sheet indicating the contribution of each team member. This sheet is to be signed by each team member, indicating her agreement that this is an accurate description of the work done by each member of the team.
The problem
Electronic Communications manufactures portable radio systems that can be used for two-way communications. The company's new product, which has a range of up to 25 miles, is particularly suitable for a variety of business and personal uses. The company can sell through any combination of the following channels:
1. marine equipment distributors
2. business equipment distributors
3. a national chain of retail stores
4. a mail order distributor
Because of differing distribution and proportional costs, the profitability of the product will vary with the distribution channel, as will the advertising costs and personnel costs for sales.
Sales through marine equipment distributors will produce a profit of $90 per unit, with advertising costs $10 per unit and 2 hours of personnel time per unit sold.
Sales through business equipment distributors produce a profit of $84 per unit, with advertising costs $8 per unit and 3 hours of personnel time required per unit sold
Sales through the national retail chain produce $70 profit per unit, with advertising costs $9 per unit and personnel time 3 hours per unit.
Sales through the mail order distributor produce a profit of $60 per unit, with an advertising cost of $15 per unit but no personnel time for sales.
There is $5000 available for advertising the new radio for the year; up to 1800 hours of personnel time can be allocated to sales. Management has decided on a production run of 600 units for the year, and a contract has been signed with the retail chain requiring at least 150 units be sold through that channel.
The marketing department has to establish a distribution strategy for the new radio to maximize profit. In addition to knowing how many radios to allocate to each distribution channel, they need to know how much of the advertising cost and how many hours of personnel time will be used in each channel.
Since all planning a year ahead is subject to some uncertainty and change, the marketing department also needs to consider what may happen if conditions change. Several specific questions that have been raised are:
1. If the number of radios to be produced is reduced from 600 to 550, what effect will this have on profits? What about an increase from 600 to 650?
2. Would an increase in the advertising budget produce an increase in profit? Would it be more than dollar for dollar (more than a dollar increase in profit for each additional dollar spent on advertising)? for how much of an increase does this answer hold?
3. Would it be worth $10 per additional hour to increase available personnel time by 20 hours?
4. If the contract with the retail outlet could be changed to allow a decrease to 100 units sold through the chain, how much would the change be worth to Electronic Communications?
5. How high would the per-unit profit on mail order sales have to go to make them worthwhile?
You should attempt to anticipate other variations that are not listed here, and indicate what effects they might have.
Maximum grade will require some consideration of possibilities, questions that are not given here as well as attention to style and focus of the report.