A small retail store wants to spend up to $$12,000$ to place ads with a local radio station. A $45-$second ad in a morning time slot costs $$1,000$ and market research suggests that the ad will be heard by $12,000$ potential customers. A $45-$second ad in an afternoon time slot costs $$2,000$ and will be heard by $16,000$ potential customers. And a $45-$second ad in an evening time slot costs $$500$ and will be heard by $6,000$ potential customers. The radio station will sell no more than $10$ ads to the store. How many ads in each time slot should the store purchase in order to maximize the potential customers who will hear the ads? What is the maximum number of listeners?

$($ Helpful Hints: $1,000x+2,000y+500z12,000$ is equivalent to $x+2y+0\mathrm{.}5z12.$ And maximizing $12,000x+16,000y+6,000z$ is equivalent to maximizing $12x+16y+6z$ if you interpret the optimal value in 'thousands' you are welcome! $)$