Linear Problems HW_6

"Beaconville "MODEL "Maximize Z 16X1 33X2 17X3 37X4 "Subject to "X1 X2 X3 X4 575 (personal contacts constraint "6X1 13X2 1320 (time during the day constraint "7X3 19X4 0 (nonnegativity constraint "DATA SOLUTION : Non-Integer "Type of Contact "Day /Phone "Day /Personal "Night /Phone "Night /Personal "Decision Variables "X1 "X2 "X3 "X4 "Donation "16 "33 "17 "37 "Resources "Resources used "Symbol "Resources Available "Personal contact "1 "1 "1 "1 "575 "575 "Time during the day "6 "13 "1320 "1320 "Time during the night "7 "19 "2580 "0 "Number of contacts during the day by personal "11 .45 "0 "Number of contacts

during the night by phone "368 .9 "0 "Number of contacts during the night by personal "0 "0 "Contacts "Day /Phone X1 "194 .7 "Day /Personal X2 "11 .45 "Night /Phone X3 "368 .9 "Night /Personal X4 "0 "Profit Z "9766 "DATA SOLUTION : Integer "Type of Contact "Day /Phone "Day /Personal "Night /Phone "Night /Personal "Decision Variables "X1 "X2 "X3 "X4 "Donation "16 "33 "17 "37 "Resources "Resources used "Symbol "Resources Available "Personal contact "1 "1 "1 "1 "574 "575 "Time during the day "6 "13 "1320 "1320 "Time during the night "7 "19 "2576 "0 "Number of contacts during the day by personal "12 "0 "Number of contacts during the night by phone "368 "0 "Number of contacts during the night by personal "0 "0 "Contacts "Day /Phone X1 "194 "Day /Personal X2 "12 "Night /Phone X3 "368 "Night /Personal X4 "0 "Profit Z "9756 "Observation "The donations computed by the non-integer solution is more than the one computed by the integer solution . This is so because the non-integer solution is not constraint by whole numbers , and thus it maximized the use of resources "Harry and Melissa Jacobson "MODEL "Maximize Z 575X1 120X2 "Subject to "30X1 18X2 480 (labor constraint "40X1 15X2 0 (demand for table "X2 /X1 4 /1 (demand for chair "X2 - 4X1 0 (demand for chair written in standard form after rearranging tha above equation "X1 , X2 0 (nonnegativity constraint "DATA SOLUTION "Product "Table "Chairs "Decision Variables "X1 "X2 "Profit "575 "120 "Resources "Resources used "Symbol "Resources Available "Labor "30 "18 "480 "480 "Material "40 "15 "460 "0 "Demand for chair "4 "0 "Product "Table X1 "4 "Chairs X2 "20 "Profit Z "4700 "Skimmer Boat Company "MODEL "Maximize Z 20500X1 12000X2 22300X3 "Subject to "1 .3X1 X2 1 .5X3 210 (capacity constraint "X1 2X3 X2 X3 (demand for bass "X1 - X2 - X3 0 (demand for bass written in standard form after rearranging tha above equation "X1 (X2 X3 2 (demand for bass "X1 - 2X2 - 2X3 0 (nonnegativity constraint "DATA SOLUTION "Boat "Bass "Ski "Speedboat "Decision Variables "X1 "X2 "X3 "Profit "20500 "12000 "22300 "Resources "Resources used "Symbol "Resources Available "Capacity "1 .313 "1 "1 .5 "210 "210 "High-powered engines "1 "2 "158 "0 "Demand for Bass "0 "0 "Boat "Bass X1 "110 "Ski X2 "31 "Speedboat X3 "24 "Profit Z "3162200...