Pixie Hollow Tea shop serves two different teas that it brews every day. Tinker$$s Dawn Brew and Red$$s Goodnight Time. Both are made up of three different ingredients Pixie Dust, Gillywater and Lost Boys London Leaves. They have enough of each brew to make up to $80$ cups of each a day but have the capacity at the tea shop to brew $200$ cups a day. Tinker$$s Dawn Brew is made up of $25\%$ Pixie Dust, $30\%$ Gillywater and $45\%$ Lost Boys London Leaves. Red$$s Goodnight Time is made up of $55\%$ Pixie Dust, $15\%$ Gillywater and $30\%$ Lost Boys London Leaves. Tinker$$s Dawn Brew sells three cups $$1\mathrm{.}95$ per cup for every two cups of Red$$s Goodnight Time $$1\mathrm{.}70$ per cup. The fairies would like to know the number of cups of each blend to sell each day in order to maximize sales.

$1.$ Formulate a linear programming model for this problem, solving it in Excel.