Goal Programming

Mackenzie owns a custom watch company, which has several different types of watches that she and her team manufacture from raw materials. Below is 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

Goal Programming Part 1

Formulate a linear program to maximize profit per week with the following constraints:

• The pressure-testing equipment can only handle 40 tests per week.
• Mackenzies supply chain restricts the availability of parts 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.

• At least 32 watches must 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.

Goal Programming Part 2

• Create a copy of the sheet Watch LP
  • Right click the tab Watch LP, click Move or Copy, Select the Watch LP sheet, click the Create a Copy checkbox and then click okay.
  • Rename the newly created sheet Watch LP2
• The following steps are to be completed in the sheet Watch LP2
  • Add the following constraint:
    • Profit should be at least $13,500
  • Run Solver. You may or may not get an infeasible solution.

Goal Programming Part 3

• Create a copy of the sheet Watch LP2
  • Right click the tab Watch LP-2, click Move or Copy, Select the Watch LP-2 sheet, click the Create a Copy checkbox and then click okay.
  • Rename the newly created sheet Watch Goal Program
• The following steps are to be completed in the sheet Watch Goal Program
  • Turn the following hard constraints into soft constraints
    • Minimum profit should be at least $13,500
    • Suppliers limit your supply of batteries to a maximum of 40 batteries per week
    • Suppliers limit your supply of internal gears to 2400 internal gears per week
  • Update cell B5 to say Minimize Percent Deviation
  • Set all values in the optimal solution row and the objective function coefficient row to show at least 4 decimal places
  • Build the goal program to minimize percent deviation.
  • Run solver.