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Q: Quantitative ( Answered ,   1 Comment )
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 Subject: Quantitative Category: Business and Money > Economics Asked by: k9queen-ga List Price: \$15.00 Posted: 03 Dec 2003 21:09 PST Expires: 02 Jan 2004 21:09 PST Question ID: 283351
 ```Cedar Point Amusement park management is preparing the parks annual promotional plan for the coming season. Several advertsing alternatives exist: Newspaper, television, radio, and displays at recreational shows. The information below shows the characteristics associated with each of the advertsing alternatives, as well as the maximum number of placements available in each medium. Given an advertsing budget of \$250,000, how many placements should be made in each medium to maximize total audience exposure? PLease show work. Type Cost Maximum Number Exposure -------------------------------------------------------------------- Newspaper 1500 100 80 Televsion 2200 50 120 Radio 750 50 45 Shows 150 3 10```
 ```k9queen, For your question, I will assume that the exposure number listed is the number of people exposed to the Cedar Point advertisement for everyone one unit of the advertising type purchased, and that this rate remains constant regardless of the number of units purchased. The first thing we need to do is analyze all types of advertising to determine what the average cost is to expose one person to Cedar Point advertising. To do this, we divide the cost of a unit of advertising by the exposure that each unit receives. In the order written above (answers rounded to the nearest cent): Newspaper: 1500 / 80 = \$18.75 per exposure Television: 2200 / 120 = \$18.33 per exposure Radio: 750 / 45 = \$16.67 per exposure Shows: 150 / 10 = \$15.00 per exposure From this, we see that we get the best value from Shows, followed by Radio, Television, and finally Newspaper advertising. Because Shows is always the best value, common sense seems to dictate that we should purchase as many units of Shows advertising as possible. Unfortunately, there are only three units available, so this is as much as we can possibly purchase. Three units of Show advertising valued at \$150 each costs \$450 total, and gains Cedar Point 30 (10*3) exposures. We now have \$249,550 (\$250,000 - \$450) remaining in our budget. The next best value comes from Radio, so we buy as much of that as possible. 50 units of Radio advertising valued at \$750 each costs \$37,500 total, and gains Cedar Point 2,250 (50*45) exposures, bringing the total of exposures to 2,280 (2,250 + 30). We now have \$212,050 (\$249550 - \$37500) remaining in our budget. The next best values comes from Television, so we buy as much of that as possible. 50 units of Television advertising valued at \$2200 each costs \$110,000 total, and gains Cedar Point 6,000 (50*120) exposures, bringing the total of exposures to 8,280 (6,000 + 2,250 + 30). We now have \$102,050 (\$212050 - \$110000) remaining in our budget. The only advertising medium remaining is Newspaper, so we spend as much of what's remaining in our budget on this. Dividing our total remaining budget of \$102,050 by the \$1,500 per unit cost of Newspaper advertising shows that we can purchase 68 Newspaper advertising units, to gain Cedar Point an additional 5,440 (68*80) exposures, bringing the total number of exposures to 13,720 (5,440 + 6,000 + 2,250 + 30). If you multiply the \$1,500 per unit cost of Newspaper advertising by the 68 units we purchased, you'll see that this total comes out to \$102,000, meaning that we still have \$50 left over. Is it possible to use this \$50 somehow to get just a little bit more exposure for Cedar Point? We've already purchased all of the other mediums available to us, but if we freed up \$1,450 worth of advertising from those other mediums, we could purchase one more Newspaper advertisement and use all of our alloted budget, and possibly pick up a few extra exposures. Since Television advertising costs more than \$1,450, the only way we could raise the money is by buying less Radio and Shows advertising. However, there is no way to factor 750 and 150 to get 1450, so it is not possible to free up exactly \$1,450. So the next step is to see if it is possible to free up \$2,950 from other advertising, so that we can purchase two additional units of Newspaper advertising to use our entire budget. With \$2,950 required, we can now free up \$2,200 by purchasing one less Television advertisement, leaving us with \$750 to raise. Since the sum of our Shows advertising is only \$450, the only way we can do this is to purchase one less Radio unit as well. So by giving up one Radio and one Television advertisement, we can use all our money to purchase two additional Newspaper advertisements. But is it worth while to do this? One Television advertisement brings 120 exposures, while one Radio advertisement yields 45, for 165 exposures lost. In exchange, we get 80 exposures per Newspaper advertisement, for 160 exposures total, five less than we had before. Even though we found a way to use our last \$50, this can only be done by reallocating funds to less effective advertising, and does not provide optimal results. Therefore, our original calculations were correct, and the optimal allocation of advertising funds is as follows: Shows: 3 (30 exposures Radio: 50 (2,250 exposures) Newspaper: 50 (6,000 exposures) Television: 68 (5,440 exposures) Total Exposures: 13,720 Total Budget Used: \$249,950 Average Cost Per Exposure (rounded to nearest cent): \$18.22 Source Referenced: Google Calculator ://www.google.com/help/features.html#calculator```
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