Downey Communications manufactures portable radio systems that can be used for two-way communications. The company has developed a new product suitable for a variety of applications. The distribution channels for the radio are as follows: 1. Marine equipment distributors 2. Business equipment distributors 3. National chain of retail stores 4. Direct mail Because of differing distribution and promotional costs, the profitability of the product will vary with the distribution channel. In addition, the advertising cost and the personal sales effort required will vary with the distribution channels. The firm has set the advertising budget at $5000 and there is a maximum of 1800 hours of sales force time available for allocation to the sales effort. Management has also decided to produce exactly 600 units for the current production period. Finally, an ongoing contract with the national chain of retail stores requires that at least 150 units be distributed through this distribution channel. The company is faced with the problem of establishing a strategy that will provide for the distribution of the radios in such a way that overall profitability of the radio production will be maximized. Distribution Channel Profit per Unit Sold Advertising Cost Per Unit Sold Personal Sales Effort/Unit Sold Marine distributors $90 $10 2 hours Business $84 $ 8 National retail store $70 $ 9 Direct mail $60 $15 3 hours 3 hours None a) What is the optimal distribution channels? How many units should be distributed to each channel? (solution) How much profit? b) Which constraints are binding? c) What would the profit per unit on mail-order distribution need to be before the company would begin using that distribution channel? d) If the profit per unit distributed through the business channel dropped $5, how would that affect the optimal values of the decision variables and the objective function? e) What would be the effect on the solution if 10 additional units were required at the retail store? f) What if 100 hours of additional sales force time was available?