$2)$ The Thermos Store would like to determine the best way to allocate a monthly advertising budget of $$10,000$ between local newspaper advertising and social media advertising. The store must spend the whole budget each month. Management decided that at least $20\%$ of the budget must be spent on each type of media, and that the amount of money spent on local newspaper advertising cannot be more than twice the amount spent on social media advertising. A marketing consultant developed an index that measures audience exposure per dollar of advertising on a scale from $0$ to $100,$ with higher volumes implying greater audience exposure. If the value of the index for local newspaper advertising is $60$ and the value of the index for social media advertising is $85,$ how should the restaurant allocate its advertising budget in order to maximize the value of total audience exposure?