Frosty$$s Snow Cones uses a weighted moving average method to forecast snow cone sales. It assigns a weight of five to the previous month's demand, three to demand $2$ months ago, and one to demand $3$ months ago. If sales amounted to $1,000$ snow cones in May, $2,200$ snow cones in June, and $3,000$ snow cones in July, what should be the forecast for August?

Group of answer choices

$2,405$

$2,061$

$3,767$

$2,511$

$1,681$