Solve this problem to optimality and answer the following questions:
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A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the
Max 35x1 + 25x2 + 15x3+ 30x4
s.t. 7x1 + 8x2 + 7x3 + 13x4 ≤ 18 {Constraint 1}
x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}
x1 + x2 ≤ 1 {Constraint 3}
x1 + x3 ≥ 1 {Constraint 4}
x2 = x4 {Constraint 5}
xj = {1, if location j is selected0, otherwisexj = 1, if location j is selected0, otherwise
Solve this problem to optimality and answer the following questions:
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- Assign nine automobile service departments to bays in a 3 × 3 grid so that the closeness ratings Problem 2 in the following matrix are satisfied. (The unimportant and ordinary-importance ratings have been omitted to simplify the example.) The location of department 4 must be in the upper right-hand corner of the grid to satisfy a town ordinance.Four qualified postgraduate students are to be allocated to four professors. The preference given by student (scale 1-10) is shown as table below. Student A В C D Professor James Jordan Janet 7 8 6. Jessy 5 8. 7 (a) Formulate a linear programming model for the problem. [NOTE: Please use x, where i = 1, 2,...,n -Professor and j=1, 2,...,m -Student to represent your decision variables.] (b) From the output below, what is the optimal allocation plan and what is the total preference scales obtained from the allocation plan? Model Variable Original Value Final Value Value x11 1 1 Value x12 1 Value x13 1 Value x14 Value x21 Value x22 Value x23 1 1 1 1 1 Value x24 1 Value x31 Value x32 Value x33 1 1 1 1 Value x34 1 Value x41 1 Value x42 1 Value x43 1 Value x44 1 1 699 445Using the grid technique to determine the least-cost location (warehouse) for this problem: Tons Rate X - Coordinates Y – Coordinates S1 200 0.5 2 14 S2 300 0.6 6 10 M1 100 1 2 2 M2 100 2 10 14 M3 100 1 14 18 M4 100 2 14 6 The Grid center coordination is ____ and _____ (round the results to 1 decimal place) Group of answer choices (9.9; 7.8) (5.5; 6.9) (8.7; 10.5) (10.5; 6.4) (9.9; 8.9)
- (Use output ranges of 2000, 4000, 6000, 8000 etc. and intervals of $50,000 on the Y axis. Output X Location A Location B Location B Location D 2 000 120 000 120 000 130 000 150 000 4 000 180 000 160 000 160 000 170 000 6 000 240 000 200 000 190 000 190 000 8 000 300 000 240 000 220 000 210 000 10 000 360,000 280 000 250 000 230 000 12 000 420 000 320 000 280 000 250 000 14 000 480,000 360 000 310,000 270 000 16 000 540 000 400 000 340 000 290 000 18 000 600 000 440 000 370 000 310 000 20 000 660 000 480 000 400 000 330 000 Over what range of output is location A the most preferred location? 2. Over what range of output is location B the most preferred location? 3.Over what range of output is location C the most preferred location?(a) Mohawk Valley Furniture Warehouse has purchased a retail outlet with six departments (A, B, C, D, E, and F), as shown below. The anticipated number of customers that move between the departments each week is given as follows: 70 and 50 customers move from department A to department B and F respectively; 100 customersmove from department B to department E; 70 customers move from department C to department B; 80 customers move from department D to department C; 40 and 30 customers move from department E to departments A and F respectively; and 60 and 100 customers move from department F to departments B and E respectively. The initial layout is given in the matrix below. (i) Construct the load summary chart for Mohawk's layout.) (ii) Evaluate the current layout in terms of non-adjacent loads.L.P. Model: Maximize Subject to: Z = 8X+6Y 1X + 2Y ≤8 5X +4Y ≤20 X,Y 20 (C₁) (C₂) On the graph on right, the constraints C, and C₂ have been plotted. Using the point drawing tool, plot the four corner points for the feasible area. The optimum solution is: X= 4 (round your response to two decimal places). Y = (round your response to two decimal places). 20- 18- 16- 14- 12+ >10- 8- 6- 0 2 4 6 8 10 X 12 14 16 18 20 2
- Define Linear programming (LP)?Oscar's Bowling, Ic., wants to break into the Phoenix metropolitan market with one of its super-sized 200 lane, 24-hour bowling alleys. It, however, only has enough capital to build one facility. Oscar wants it to be centered by population, as determined by the center of gravity method. The following information is given: City Population x coordinate y coordinate Tempe 285,000 Scottsdale 350,000 10 Chandler 725,000 5 Mesa 300.000 10 1 Glendale 345,000 1 10 a. Where should Oscar build? Oscar should build at an x coordinate of and a y coordinate of . (Enter your responses rounded to one decimal place.)A new stadium complex is being planned for Denver, and the Denver traffic engineer is attempting to determine whether the city streets between the stadium complex and the interstate highway can accommodate the expected flow of 21,000 cars after each game. The various traffic arteries between the stadium (node 1) and the interstate (node 8) are shown in the following 1 10 8 7 0 1 LO 5 0 N 3 3 4 CO 6 6 LO 5 4 5 0 0 0 2 LO 6 26 2 7 8 4 9 0 0 8 The flow capacities on each street are determined by the number of available lanes, the use of traffic police and lights, and whether any lanes can be opened or closed in either direction. The flow capacities are given in thousands of cars. Determine the maximum traffic flow the streets can accommodate and the amount of traffic along each street. Will the streets be able to handle the expected flow after a game? Hint: I would use LP to solve it.
- Suppose the following costs for a 10-hour round-trip flight apply to the time frame and expenses of an unscheduled 5-hour charter flight from Baltimore to Las Vegas (and return the next day) on a seven-year-old Boeing 737–800 with 120 occupied seats. Some costs listed in the table have been aggregated up to the flight level from a seat-level decision where they are incurred. Others have been allocated down to the flight level from an entry/exit or maintain-ownership company-level decision. Still other costs vary with the go/no go flight-level decision itself. Your job is to analyze each cost item and figure out the “behavior of cost”—that is, with which decision each cost varies. Fuel and landing fees =$5,200 Quarterly airframe maintenance re: FAA certificate = $1,000 Unscheduled engine maintenance per 10 flight hours =$1,200 Pro rata time depreciation for seventh year of airframe = $7,200 Flight pay for pilots per round-trip flight = $4,200 Long-term hangar facility lease = $6,600…Maximize f = x + y subject to the following constraints: x + 2y ≤ 8 -2x + 3y ≤ 2 x ≤ 4 ≤ x 0 ≤ yAn oil company is considering two sites on which to drill. The sites are described in the foliowing table. Complete parts (a) through (b) below. Site A Profit if ol is found: $120 million Loss if no oil is found: $20 million Probablity of finding oil: 0.2 Site B: Profit if ol is found: $180 million Loss if no oil is found: $30 milion Probability of finding oil: 0.1 a. Which site has the larger expected profit? Site A has the larger expected profit. Site B has the larger expected profit. The expected profits for both sites are the same. b. If the expected profit for both sites is not the same, by how much is the expected profit larger? milion (Round to the nearest tenth as needed.)