Sew & Sew Inc. manufactures pants and vests. The profit on each pair of pants is $6 and on each vest is $5. The pants use 2 yards of material and the vests use 1.5 yards of material each. Because of productions limitations, Sew & Sew cannot manufacture more than 10 of these garments per day and cannot use more than 18 yards of material per day. If Sew & Sew can sell all the pants and vests it makes, find the number of each garment is should produce per day to maximize its profit.

let pants = x

vest = y

cloth = 2x + 1.5y

x+y=10

2x + 1.5y = 18

=> 20 - 2y + 1.5y = 18

=> y = 4

x=6

pants = 6

vests = 4

profit = $56