Question

MacKenzie owns a custom watch company, and has several different types of watches that she and her team manufacture from raw materials. Below you will find a table with the watch characteristics and descriptions.

	X1	X2	X3	X4	X5	X6	X7
	Diver - Automatic	Aviator	Chronograph	Sports	High-Impact	Casual	Luxury
Profit per watch	$310.00	$270.00	$295.00	$200.00	$170.00	$100.00	$320.00
Pressure-Tested	X			X	X		X
Battery		X	X	X	X	X	X
Internal Gears	76	65	67	58	28	20	55
Knobs	1	3	4	3	2	1	3
Hands	2	5	6	5	2	2	5
Leather Band		X	X				X
Stainless Steel Band	X				X	X
Rubber Band				X
Steel (lbs)	0.7	0.4	0.4		0.5	0.1	0.35
Aluminum (lbs)		0.1	0.2	0.3	0.1	0.1	0.25
General Labor Hours	6	7	5	4	4.5	3	8
Embellishment Hours	1.5	2	2	0.5	1	0.5	3.5
Inspection Hours	0.6	0.4	0.5	0.15	0.25	0.3	0.65
Impact Resistant	X	X		X	X		X
Rotating Bezel	X	X	X

Formulate a linear program with the variables and the table to Maximize profit per week with the following constraints

• The pressure-testing equipment can only handle 40 tests per week
• MacKenzie’s supply chain restricts parts availability to 40 watch batteries, 2400 internal gears, 120 knobs, 200 hands, 25 leather bands, 35 stainless steel bands, 15 rubber bands, 20 pounds of steel, and 8 pounds of aluminum each week.
• General Labor is limited to 270 hours per week; Embellishment labor is limited to 80 hours per week, and Inspection Hours are limited to 25 per week

Additionally

• At least 32 watches much be impact resistant
• At least 15 of the watches must have a rotating bezel
• Each watch must have a minimum of 5 manufactured per week

Answer 1

From the given variables and the data, we have constructed the required linear programming problem.