A company is trying to determine how to allocate its $$78,100$ advertising budget for a new product. The company is considering newspaper ads and television commercials as its primary means for

advertising. The following table summarizes the costs of advertising in these different media and the number of new customers reached by increasing amounts of advertising.

For instance, each of the first $10$ ads the company places in newspapers will cost $$1,000$ and is expected to reach $900$ new customers. Each of the next $10$ newspaper ads will cost $$900$ and is

expected to reach $700$ new customers. Note that the number of new customers reached by increasing amounts of advertising decreases as the advertising saturates the market. Assume the company

will purchase no more than $30$ newspaper ads and no more than $15$ television ads. $($Let $N_1$ be the number of newspaper ads purchased at $$1,000$ each. Let $N_2$ be the number of newspaper ads

purchased at $$900$ each. Let $N_3$ be the number of newspaper ads purchased at $$800$ each. Let $T_1$ be the number of television ads purchased at $$12,000$ each. Let $T_2$ be the number of television ads

purchased at $$10,000$ each. Let $T_3$ be the number of television ads purchased at $$8,000$ each.$)$