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 $0.80 per pound. Revenue and other details for each product are given in the table below.

Formulate and solve the math optimization model which will maximize overall profit by determining the mix of the seven products to be produced this month. Maggie’s has certain other restrictions which must be reflected in your solution. These are:

i. At most 2000 mugs in total (combined for all types of mugs) can be sold.

ii. At least 5% of all hand warming mugs produced must be left-handed mugs.

iii. At most 15% of all hand warming mugs produced can be left-handed mugs.

iv. At least 350 hand warming mugs of both types should be produced.

v. The number of wolf mugs produced must be greater than or equal to the number of cat mugs produced.

vi. The number of standard mugs produced must be equal to or greater than the total number of wolf mugs and cat mugs combined.

vii. The number of bowls produced must be equal to or greater than the number of serving trays

viii. The number of bowls cannot exceed 400.

ix. Formulate and solve the math optimization model which will maximize overall profit by determining the mix of the seven products to be produced this month. Maggie’s has certain other restrictions which must be reflected in your solution. These are:

x. At most 2000 mugs in total (combined for all types of mugs) can be sold.

xi. At least 5% of all hand warming mugs produced must be left-handed mugs.

xii. At most 15% of all hand warming mugs produced can be left-handed mugs.

xiii. At least 350 hand warming mugs of both types should be produced.

xiv. The number of wolf mugs produced must be greater than or equal to the number of cat mugs produced.

xv. The number of standard mugs produced must be equal to or greater than the total number of wolf mugs and cat mugs combined.

xvi. The number of bowls produced must be equal to or greater than the number of serving trays

xvii. The number of bowls cannot exceed 400.