< 4_588664739525... Q : b. What is the minimum number of exams that the Professor is required to re-grade? (1 point) 4. A Municipality Office of a small town has built a new elementary school so that the town now has a total of four schools, namely: Addis Finot, Ewuqet Birhan, Netsebraq and Abrehot. Each has a capacity of 400 students. The school wants to assign children to schools so that their travel time by bus is as short as possible. The school has partitioned the town into five districts conforming to population density-north, south, east, west, and central. The average bus travel time from each district to each school is shown as follows: District Addis Finot Travel Time (min.) Ewuqet Birhan Student Netsebraq Abrehot Population North 12 23 35 17 350 South 26 15 21 27 340 East 18 20 22 31 360 West 29 24 35 10 260 Central 15 10 23 16 290 a. Determine the initial feasible solution using the Least Cost Method (LCM). (2 Points) b. Determine the optimal number of children that should be assigned from each district to each school to minimize total student travel time using the Stepping Stone Method. (2 Points) 5. CORD Pharmaceuticals has four manufacturing plants: A, B, C and D, each of which can produce any one of four products P1, PII, PIII, and PIV. The net profit contribution from each plant-product assignment is given below (in USD). Considering the data below, answer the questions that follow. Products Plants P. PII PIII PIV Plant A 7 5 8 2 Plant B 7 8 9 4 Plant C 3 5 7 9 Plant D 5 5 6 7 a. Obtain which product each plant should produce to maximize the profit, and determine the maximum earning. (2 points) b. If 'Plant C' is unavailable due to unexpected shutdown and, thus can't operate, what will be the revised set of assignment? (2 points) 2 6. Lidet EtFruit is a small private firm working on the marketing of several farm produces with red palm fruit on top of its retail priorities. Even though it is required by many business customers throughout the year, its demand is documented to be on its peak during the Ramadan fasting season. Lidet Etfruit is contemplating to acquire the fruit from its loyal and dependable supplier, Dalol Fruits Farming SC., operating in Afar region. Lidet Etfruit is well informed that the fruits must be ordered three days in advance from its supplier in order to obtain the amount it requires. Although Ramadan is fast-approaching sales are almost entirely eleventh-hour, impulse purchases. Advance sales are so small that the firm has no way to estimate the probability of low (25 kg), medium (60 kg), or high (130 kg) demand for red palm fruits on the day of Ramadan. The firm buys the fruits for $15/kg and sells them for $40/kg. Considering the information given above, do the following. a. Construct a payoff table for the problem. (2 points) b. Determine the best investment using the following criteria. (1 point each) Maximin Minimax egret The Hurwicz criterion (ass 7. A farm owner is going to erect a mainten ing with a connecting electrical generator and water tank. The activities, activity descriptions, and estimated durations are given in the table: 2/3 < 4_588664739525... @ Q : Plant D 5 a. Obtain which product each plant should produce to maximize the profit, and determine the maximum earning. (2 points) b. If 'Plant C' is unavailable due to unexpected shutdown and, thus can't operate, what will be the revised set of assignment? (2 points) 2 6. Lidet EtFruit is a small private firm working on the marketing of several farm produces with red palm fruit on top of its retail priorities. Even though it is required by many business customers throughout the year, its demand is documented to be on its peak during the Ramadan fasting season. Lidet Etfruit is contemplating to acquire the fruit from its loyal and dependable supplier, Dalol Fruits Farming SC., operating in Afar region. Lidet Etfruit is well informed that the fruits must be ordered three days in advance from its supplier in order to obtain the amount it requires. Although Ramadan is fast-approaching sales are almost entirely eleventh-hour, impulse purchases. Advance sales are so small that the firm has no way to estimate the probability of low (25 kg), medium (60 kg), or high (130 kg) demand for red palm fruits on the day of Ramadan. The firm buys the fruits for $15/kg and sells them for $40/kg. Considering the information given above, do the following. a. Construct a payoff table for the problem. (2 points) b. Determine the best investment using the following criteria. (1 point each) Maximin Minimax egret The Hurwicz criterion (assume =0.6) 7. A farm owner is going to erect a maintenance building with a connecting electrical generator and water tank. The activities, activity descriptions, and estimated durations are given in the table: Activity Activity Description Activity Predecessor Activity Duration (weeks) A Excavate 2 B Erect building A 6 C Install generator A 4 D Install tank A 2 E Install maintenance equipment B 4 F Connect generator and tank to building B,C,D 5 G Paint finish B 3 H Checkout facility E.F 2 a. Draw the project network using the Activity on Node (A-O-N) convention. (2 points) b. Compute the float (slack time) time of each activity. (2 points) C. Determine the critical path and calculate the project completion time. (1 point) 3 2/3 3/3 < 4_588664739525... Q : Instruction: Go through the workout questions given below, read them carefully, and solve them using appropriate mathematical techniques with all necessary steps involved. 1. Electra Inc. promotes its products from a large city to different parts in the state. Electra has budgeted up to $8,000 per week for local advertising. The money is to be allocated among four promotional media: TV spots, newspaper ads, and two types of radio advertisements. Electra's goal is to reach the largest possible high-potential audience through the various media. The following table presents the number of potential customers reached by making use of an advertisement in each of the four media. It also provides the cost per advertisement placed and the maximum number of ads that can be purchased per week. audience reached cost per Medium per ad ad ($) TV spot (1 minute) 5,000 800 maximum ads per week 12 Daily newspaper (full-page ad) 8,500 925 5 Radio spot (30 seconds, prime time) 2,400 290 25 Radio spot (1 minute, afternoon) 2,800 380 20 Electra's contractual arrangements require that at least five radio spots be placed each week. To ensure a broad-scoped promotional campaign, management also insists that no more than $1,800 be spent on radio advertising every week. Formulate this problem as a LPP (3 points). 2. Domestic cows can be bought for $200 each but Hybrid cows cost $500 each. The domestic cows produce 30 gallons of milk per week and the Hybrid ones produce 50 gallons of milk per week. A gallon of milk can be sold for $3. A cow costs $100 per week to feed. If the financial constraint is to spend $8000 for cows and the capacity constraint is that total number of cows to be bought cannot exceed 20 cows. Formulate a linear programming model for this problem, and find the optimal combination of domestic and hybrid cows that maximize the total profit earned using the graphic Method (4 Points). 3. Professor Wang teaches two sections of operations management, which combined will result in 130 final exams to be graded. Professor Wang has two graduate assistants (GAs), James and Ann, who will grade the final exam. There is a 3-day period between the time the exam is administered and when final grades must be posted. During this period James has 14 hours available and Ann has 12 1 available hours to grade the exams. It takes James an average of 8.4 minutes to grade an exam, and it takes Sarah 15 minutes to grade an exam; however, James's exams will have errors that will require Professor Wang to ultimately re-grade 12% of his exams, while only 5% of Ann's exams will require re-grading. Professor Wang wants to know how many exams to assign to each GA to grade in order to get all of them graded, but she also wants to minimize the number of exams that she will be required to re-grade. a. Formulate an LP Model for the problem, and determine the optimal number of exams that should be assigned to each GA to grade? Solve it using the Simplex Method. (4 Points) b. What is the minimum number of exams that the Professor is required to re-grade? (1 point) 4. A Municipality Office of a small town has built a new elementary school so that the town now has a total of four schools, namely: Addis Finot, Ewuqet Birhan, Netsebraq and Abrehot. Each has a capacity of 400 students. The school wants to assign children to schools so that their travel time by bus is as short as possible. The school has pa population density-north, south, east, wes district to each school is shown as follows: the town into five districts conforming to The average bus travel time from each Travel Time (min.) Student 1/3