Linear programing - Assignment Example

Linear programming individual assignment Electronic Components Inc. manufactures a new radio system suitable for a variety of business and personal uses. The distribution channels for the new radio are:1.- Marine equipment distributors.2.- Business equipment distributors.3.- National chain of retail stores.4.- Mail order.Because of differing distribution and promotional costs, the profitability of the product will vary depending on the distribution channels chosen, because of a difference in the promotional costs.

In addition, the advertising cost and the personal sales effort required will also vary. The following table summarizes the contribution to profit, advertising cost, and personal sales effort for each channel (the profit per unit sold includes all the cost, including the advertising cost per unit sold):Distribution channelProfit per unit soldAdvertising cost perPersonal sales effortunit soldper unit soldMarine distributors$90$102 hoursBusiness distributors$84$83 hoursNational retail stores$70$93 hoursMail order$60$15NoneThe firm has set the advertising budget at $5.

000, and a maximum of 1.800 hours of sales force time is available for allocation to the sales effort. The General Manager has also decided to produce 600 units for the current production period. Finally, an ongoing contract with the business distributors requires that at least 150 units have to be distributed through this distribution channel. The problem is to establish the distribution strategy for the radios that will maximize overall profitability of the new radio production.1.- Write down the objective function and all the restrictions.

The restrictions are:1. The maximum budget is 1.500 dollars 2. The maximum time is 1.800 hours3. The units that are produce equal to 600 units4. The 150 units must be distributed through this channel2.- In the next page you have three sensibility analysis.a) Identify the real one and why is it that one. The sensibility analysis option 1 can be identified as being the real one. This is because it contains no negative values for all the deliverables.b) Which is the best combination in terms of distribution channel to maximize the total profit and which is that maximum profit?

The best combination for the distribution of channels is option 1 and 2 in order to maximize the total profits.The total profits incurred are:c) If a change in the marine distributors channel took place and the profit per unit fell to $80, would the optimal solution change?. Why? If a change in the marine distributors channel took place and the profit per unit fell to $80, the optimal solution changes and the total maximum profit is reduced. This can be attributed to the fact that $80 is an objective function and thus has an effect on the entire value of profit incurred. d) Having the possibility of increasing the advertising budget, which would be the perfect increase in %?

Having the possibility of increasing the advertising budget, the perfect increase would be obtained by correlating the maximum increase to the full value:e) Which would be the impact of producing two units for the mail order distribution channel? Producing two units for the mail order distribution channel results into an increase in the advertising, the sales effort also increases, the production units’ decreases and the business retail restriction increases. The non positive values will be eliminated and hence the scenario described above.f) The marketing director is thinking about changing the Business distributor’s restriction and increases it from 150 units to 300 units.

How is this going to affect the optimal solution? Why? If the marketing director changes the Business distributor’s restriction and increases it from 150 units to 300 units, this will increase the cost of advertisement and hence the cost of production but no major increases will result on the final sales. The resulting profits do not increase and in some scenarios losses may be incurred.g) There is a possibility about a new distribution channel. If it has the same personal sales effort and advertising cost of the Mail order, but a profit per unit of $110, would you recommend it?

Would the optimal solution change? Why? It would not be recommended that a new distribution channel which has the same personal sales effort and advertising cost of the Mail order. The optimal solution would not change of the number of units’ personal sales per unit sold remains zero. The absence of any value on the personal sales per unit sold has an effect in the optimal solution and resulting in null values.