6.15. You need to take a trip by car to another town that you have never visited before. Therefore, you are studying a map to determine the shortest route to your destination. Depending on which route you choose, there are five other them A. B. C, D. E) through which you might pass on the way. The map shows the mileage along each road that directly connects two towns without any intervening towns. These numbers are summarized in the following table, whe indicates that there is no road directly connecting these two towns without going through any other towns. Miles between Adjacent Towns Town A B D E Destination Origin 40 60 50 10 70 20 55 40 50 D 10 60 80 Тext b. Formulate and solve a spreadsheet model for this problem.
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- 1. A city is reviewing the location of its fire stations. The city is made up of a number of neighborhoods, as illustrated in the figure below. A fire station can be placed in any neighborhood. It is able to handle the fires for both its neighborhood and any adjacent neighborhood (any neighborhood with a non-zero border with its home neighborhood). The objective is to minimize the number of fire stations used. Solve this problem. Which neighborhoods will be hosting the firestations?27 In order to manufacture 3,000 pairs of shoes in a week, a firm can use 3,000 workers and 100 machines or 200 machines and 4,000 workers Which method is considered more technically efficient? a 4,000 workers and 200 machines b Both are equally efficient c 3,000 workers and 100 machines d Neither could be considered efficient 33 A manufacturing business can use 100 workers and 20 machines, 140 workers and 18 machines, or 150 workers and 18 machines to produce 80 chairs If each worker costs $40 and each machine is rented for $1000, the economically efficient input combination is: a 100 workers and 20 machines b 150 workers and 18 machines c none of these input combinations d 140 workers and 18 machines2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed…
- 11. For a product mix linear programming problem, we use three materials (A, B and C) to make two products (X and Y) to maximize total profit. The following screenshot is the Answer Report generated by Excel. Given above report, which statement is FALSE? Select one: a. The Material C is used up given the optimal solution. b. The optimal solution is making 5 units of Product X only. c. The Material B is used up given the optimal solution. d. The optimized (maximum) profit is $60Problem 3: Let L(x, y) be the statement “x loves y”, where the domain for both x and y consists of all people in the world. Use quantifiers to express each of the following statements.1. Everybody loves Jerry.2. Everybody loves somebody.3. There is somebody whom everybody loves.4. Nobody loves everybody.5. There is somebody whom Lydia does not love.6. There is somebody whom no one loves.7. There is exactly one person whom everybody loves.8. There are exactly two people whom Lynn loves.9. Everybody loves himself or herself.10. There is someone who loves no one besides himself or herself.1. For each statement specify whether it is True or False? MLP solver is a heuristic method. A local optimum is better than all nearby points. An optimization problem can only have one local optimal solution. A global optimum is the best point in the entire feasible region. An optimization problem can only have one global optimal solution. For linear optimization problems any local optimal solution is a global optimal solution. For some nonlinear programming problems, Solver can get stuck at a local optimum and never find the global optimum. Forsomelinearprogrammingproblems,Solvercangetstuckatalocaloptimumandnever find the global optimum. Solver is guaranteed to find the global optimum for convex nonlinear optimization problems. A heuristic is a relatively simple solution method that often provides good but not necessarily optimal solutions. MLP solver is a heuristic method.
- 2. A canning company produces two sizes of cans—regular and large. The cans are produced in 10,000-can lots. The cans are processed through a stamping operation and a coating operation. The company has 30 days available for both stamping and coating. A lot of regular-size cans require 2 days to stamp and 4 days to coat, whereas a lot of large cans requires 4 days to stamp and 2 days to coat. A lot of regular-size cans earn $800 profit, and a lot of large-size cans earn $900 profit. In order to fulfill its obligations under a shipping contract, the company must produce at least nine lots. The company wants to determine the number of lots to produce of each size can (and) in order to maximize profit. 8. In Problem 2, how much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?Find the minimum value of the function z=2x+2y subject to the following constraints. x≤17 y≤16 5x+2y≥42 3x+11y≥841. Klara started working at a deli shop on April 1, 2020. On October 19, 2020 she informed her employer that she is pregnant and is due on February 1, 2021. Her employer informed her that they are not able to provide her any paid time off since it is a very small shop. They will, however, provide her with unpaid time off if she needs it. She has indicated that she would like to take her pregnancy leave starting November 2. Klara is concerned that the deli is hiring someone to replace her when she is on her leave. Which of the following is true: A. Klara has a right to her job back when her leave is over unless the position no longer exists for reasons other than Klara taking a leave. B. Klara is entitled to 17 weeks of pregnancy leave and up to 78 weeks of maternal leave. C. Klara is entitled to 17 weeks of pregnancy leave but all of her pregnancy leave Thust be taken before the birth of her baby D. Klara is entitled to 17 weeks of pregnancy leave and 63 weeks of parental leave. 2.…
- Problem: Acme Manufacturing produces widgets on an assembly line. The assembly process has five tasks, each with its own processing time: Task Processing Time (Seconds) A 10 B 8 C 12 D 9 E 7 drive_spreadsheetExport to Sheets Acme currently has two workers assigned to the assembly line, and they work simultaneously. The company wants to improve line efficiency and reduce waste. Objective: Balance the assembly line by assigning tasks to each worker in a way that minimizes idle time and maximizes output.Same situation as in the previous two problems this time the magnet s mass is 5.68 kg and the magnetic force pulling it to the right is 170.9 N. The length of the cord is 1.70 m, and the ceiling is 2.98 m above the floor. Suppose that you cut the cord and the magnet falls to the floor while still being pulled to the right by the force of 170.9 N. How long will it take the magnet to hit the floor? 0.848 s 0.403 s 0.707 s 0.495 sA machine shop manufactures two types of bolts. The bolts require time on each of the three groups of machines, but the time required on each group differs, as shown in the table below. Type I Type IIMachine 1 0.2 min 0.2 minMachine 2 0.6 min 0.2 minMachine 3 0.04 min. 0.08 min Production schedules are made up one day at a time. In a day, 300, 720, and 100 minutes are available, respectively, on these machines. Type I bolts sell for 15¢ and type II bolts for 20¢. (a) How many of each type of bolt should be manufactured per day to maximize revenue?(b) What is the maximum revenue?(c) Suppose the selling price of type I bolts began to increase. Beyond what amount would this price have to increase before a different number of each type of bolts should be produced to maximize revenue?