A firm has prepared the following binary integer program to evaluate a number of potentia goal is to maximize the net present value of their decision while not spending more than th Max 35x1 + 35x2 + 20x3+ 30x4 s.t. 12x1 +10x2 + 4x3 +13x4 $ 18 (Constraint 1} x1 + x2 + x3 + x4 2 2 {Constraint 2) x1+ x2 S 1 {Constraint 3} X1 + x3 2 1{Constraint 4} x2 = x4 (Constraint 5} S1, if location j is selected 10, otherwise Solve this problem to optimality and answer the following questions: a. Which of the warehouse locations will/will not be selected?
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- Jk.335. Propiem 14-8 Rent'R Cars is a multisite car rental company in the city. It is trying out a new "return the car to the location most convenient for you" policy to improve customer service. But this means that the company has to constantly move cars around the city to maintain required levels of vehicle availability. The supply and demand for economy cars, and the total cost of moving these vehicles between sites, are shown below. From To A B C Demand D $9 9 5 50 From/To $8 Candidate solution A B C Total shipped Cost A - B C Total costs 8 3 60 $6 8 3 25 $5 D 0 10 a. Find the solution that minimizes moving costs using Microsoft Excel. (Leave no cells blank - be certain to enter "0" wherever required.) Supply 50 40 75 30 165 165 E F G Supply $9-43. Northwest University is in the process of complet-ing a computer bus network that will connect com-puter facilities throughout the university. The prime objective is to string a main cable from one endof the campus to the other (nodes 1–25) throughunderground conduits. These conduits are shownin the network below; the distance between them isin hundreds of feet. Fortunately, these undergroundconduits have remaining capacity through which thebus cable can be placed.(a) Given the network for this problem, how long (inhundreds of feet) is the shortest route from node1 to node 25?(b) In addition to the computer bus network, a newphone system is also being planned. The phonesystem would use the same underground conduits. If the phone system were installed, the follow-ing paths along the conduit would be at capacity and would not be available for the computer busnetwork: 6–11, 7–12, and 17–20. What changes(if any) would you have to make to the pathused for the computer bus if the phone…(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?
- 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 445b) A factory is going to modify of a plant layout to install four new machines M₁, M2, M3 and M4. There are 5 vacant places J, K, L, M and N available. Because of limited space machine M₂ cannot be placed at L and M3 cannot be placed at J. The cost of locating machine to place in Shillings is shown below: M₁ M₂ M3 M4 J Kshs '000' 24 28 K Kshs '000' 18 18 22 16 L Kshs '000' 22 28 24 M Kshs '000' 30 20 22 14 N Kshs '000' 22 18 14 16 Required: Determine the optimal assignment schedule in such a manner that the total costs are kept at a minimum.Southern Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources-rubber and leather. The resource requirements for each product and the total resources available are as follows: Product Resource Requirement per Unit Rubber (lb.) Basketball 4 Football 5 Total Resources available 500 lb. 800 ft.2 * Each basketball produced results in a profit of $12, and each football earns $16 in profit. b. Transform this model into standard form Leather (ft.2) 3 2 a. Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profit.
- A Manager has the problem of assigning four new machines to three production facilities. The respective profits derived are as shown. If only one machine is assigned to a production facility, determine the optimal assignment. Profits (K’000) production facility Machine A B C A 10 10 14 B 10 11 13 C 12 10 10 D 13 12 11Using 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)4. Optimal Rental Decisions in Cloud Computing Assume that AWS has the following 3 options for renting servers. Fraction of Job in one Server Description Rental Low Power Medium Power High Power $2/hr. $4/hr. $9/hr. Hour 1/8 1/6 1/3 L M Note that if you rent a server for less than one hour, you still must pay the rent for the entire hour. You have a job that must finısh in at most 5 hours. The low-power server can finish 1/8th of the job in 1 hour, the medium-power server can finish 1/6 of the job in one hour, and the high- power server can finish 1/3rd of the job in one hour. (a) The typical practice used by most firms is to find a single server that can do the work at the least cost and within the available time. Find the best sıngle server solution-that is, which single server should you use and for how many hours will you rent this server?
- A company with a network of 10 pipelines transports mango juice according to the details shown in Table 1. Determine the maximum flow per hour. 1. Table/Jadual 1 Сарacity Node Node (m3/h) 140 100 120 100 120 80 110 100 100 100 Reverse Capacity |(m³/h) 60 20 40 40 40 20 30 40 60 60 Start End Pipeline 1 2 3 4 1 1 1 2 3 4 6 6 7 3 7 7 8 8 10Please show how to solve bDefine Linear programming (LP)?