$1.$ Maggie$$s Pottery Barn is a mid$-$sized pottery shop selling handmade pottery to tourists in Cherokee, North Carolina. Seven products of interest are $1)$ standard clay mugs, $2)$ wolf mugs, $3)$ cat mugs, $4)$ right$-$handed hand warmer mugs, $5)$ left$-$handed hand warmer mugs, $6)$ clay serving trays, and $7)10-$inch clay bowls. $($Some of these products are shown in the embedded document below.$)$ The products are made and fired in Maggie$$s shop where tourists can watch, and then sold to tourists in a showroom. Maggie$$s currently has $27$ full$-$time employees working $8$ hours each day for $22$ days per month. Employees are paid $$12$ per hour. For the current month Maggie$$s has $6$ tons of clay, costing $$0\mathrm{.}80$ per pound. Revenue and other details for each product are given in the table below.