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- Maximize P = x + 4y − 2z subject to 3x + y − z ≤ 40 2x + y − z ≤ 20 −x + y + z ≤ 40 x ≥ 0, y ≥ 0, z ≥ 0The Bayside Art Gallery is considering installing a video camera security system to reduce its insurance premiums. A diagram of the eight display rooms that Bayside uses for exhibitions is shown in the figure below; the openings between the rooms are numbered 1 through 13. Entrance Room 1 Room 2 1 4 8 12 Room 3 Room 4 7 Room 5 10 Room 6 2 5 13 Room 7 11 Room 8 A security firm proposed that two-way cameras be installed at some room openings. Each camera has the ability to monitor the two rooms between which the camera is located. For example, if a camera were located at opening number 4, rooms 1 and 4 would be covered; if a camera were located at opening 11, rooms 7 and 8 would be covered; and so on. Management decided not to locate a camera system at the entrance to the display rooms. The objective is to provide security coverage for all eight rooms using the minimum number of two-way cameras.2. Maximize subject to p = x + 2y X +3y24 2x + y 18 x ≥ 0, y ≥ 0.
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- L.P. Model: Minimize Subject to: Z = 24X + 15Y 7X+11Y 288 16X+4Y≥64 X,Y 20 On the graph on right, constraints C, and C, have been drawn. Using the point drawing tool, plot all the corner points for the feasible area. (C₁) (C₂) 24- 22- 20- 18- 16- 14- 12- 104 8 6- 4- 2- 0+ 0 2 4 6 8 10 12 14 16 18 20 22 24 X Q Sa.) in table 1, the transportation cost is?b.) in the evaluation of occupied cells in table 1, the value of W2 is?c.) in yhe evaluation of vacant/unoccupied cells in table 1, the highest negative index is?d.) in table 2, the tiles manufactured by PlantB will be supplied to distributor?e.) the transportation cost in table 2 is?f.) in the evaluation of occupied cells in table 2, the value of V2 is?g.) in the evaluation of occupied cells in table 2, the value of W3 is?h.) in the evaluation of unoccupied/vacant cells in table 2, the highest negative index is?i.) the optimal solution is found in table? **Note: find for the tables**a.) in table 1, the transportation cost is? b.) in the evaluation of occupied cells in table 1, the value of W2 is? c.) in yhe evaluation of vacant/unoccupied cells in table 1, the highest negative index is? d.) in table 2, the tiles manufactured by PlantB will be supplied to distributor? e.) the transportation cost in table 2 is? f.) in the evaluation of occupied cells in table 2, the value of V2 is? g.) in the evaluation of occupied cells in table 2, the value of W3 is? h.) in the evaluation of unoccupied/vacant cells in table 2, the highest negative index is? i.) the optimal solution is found in table? **Note: find for the tables**