Required: • Set up the linear programming model. • Determine the product mix that produces the maximum profit for RDL corporation using: - Graphical Solution Method > Simplex Method
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- A consulting firm has four projects to consider. Each project will require time (in days) in the next three months according to the table below. Project Time in first month Time in second month Time in third month Revenue A 6 8 6 22000 B 5 6 8 18000 C 8 7 6 16000 D 5 5 4 15000 Revenue from each project is also shown. There is 20 days’ time available in the first month, 22 days’ time available in the second month, and 22 days’ time available in the third month to do these projects. The management wants to select at most 3 projects. If project B is selected, then project C must also be selected. The objective of the firm is to maximize the total revenue. Formulate an integer optimization model for this problem by defining the decision variables, the objective function and all the constraints.…Finco has the following investments available:Investment A For each dollar invested at time 0, we receive $0.10 at time 1 and $1.30 at time 2. (Time 0 =now;time= 1 one year from now; and so on.)Investment B For each dollar invested at time 1, we receive $1.60 at time 2.Investment C For each dollar invested at time 2, we receive $1.20 at time 3.At any time, leftover cash may be invested in T-bills, whichpay 10% per year. At time 0, we have $100. At most, $50can be invested in each of investments A, B, and C. Formulate an LP that can be used to maximize Finco’s cash onhand at time 3.The manager of a medical center wants to schedule staff based on a pattern of 5 days working and 2 consecutive days off. Based on the history of their workload, below is their weekly staff requirement: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Staff needed 6 5 4 4 6 4 3 a. Determine what days employee 3 does not need to work. multiple choice Saturday and Sunday Monday and Friday Tuesday and Thursday Wednesday and Friday b. Determine the minimum number of full time staff. c. Determine the minimum number of part time staff. Prev Question 9 of 10 Total9 of 10 Visit question mapNext
- Sunseel Industries produces two types of raw materials, A and B, with a production cost of $4 and $8 per unit, respectively. The combined production of A and B must be at least 700 units per month. The factory is expected to produce at least 400 units of B and not more than 1200 units of A each month. The processing times for A and B are observed to be 5 hours and 4 hours, respectively. A total of 3000 production hours are available per month. Develop a linear program that Sunseel Industries can use to determine the number of units of each raw material to produce that will meet the demand and minimize the total cost.Amy Zeng, owner ofZeng's Restaurant Distributions,supplies nonperishable goods to restaurants around the metroarea. She stores all the goods in a storage area with a single dockand one aisle. The goods are divided into five categories accordingto the following table. The table indicates the number of tripsper month to store or retrieve items in each category, as well asthe number of storage blocks taken up by each. The following picture of the storage area provides an identificationnumber for each of the 16 storage blocks. For each item category,indicate into which blocks it should be stored.A toy manufacturer preparing a production schedule for two new toys, trucks spinning tops,must use the information concerning their construction times below.Machine A Machine B FinishTruck 2hr 3hr 5hrSpinning Top 1hr 1hr 1hrFor example, each truck requires 2 hours on machine A. The available employee hours per weekare as follows: For operating machine A; 80 hours; for B, 50 hours; for finishing 70 hours. If theprofits on each truck and spinning top are R7 and R2, respectively, how many of each toyshould be made per week to maximize profit? What is the maximum profit?
- Barb’s Beach Bar operates seven days per week. Barb usesonly full-time employees and wants each employee to have twoconsecutive days off each week. She believes that she needs aminimum of three employees on Monday, Tuesday, Wednesday,Th ursday, and Sunday. On Friday and Saturday, she believes thatshe needs six employees. Develop a workforce schedule for Barb.Airline Scheduling. Alpha Airline wishes to schedule no more than one flight out of a given airport to each of the following cities: C, D, L, and N. The available departure slots are 8 a.m., 10 a.m., and 12 noon. Alpha leases the airplanes at the cost of $5000 before and including 10 a.m. and $3000 after 10 a.m., and is able to lease at most two per departure slot. Also, if a flight leaves for location N in a time slot, there must be a flight leaving for location L in the same time slot. The expected profit (in $1000) contribution before rental costs per flight is shown in the table below. Time Slot 8 10 12 C 10 6 6 D 9 10 9 L 14 11 10 N 18 15 10 a) Formulate an integer linear program model that can be used to find the profit-maximizing schedule. Define your decision variables as Xij = 1 if a flight to destination i occurs in time slot j and Xij = 0 otherwise; and Yj = number of airplanes rented for time slot j. Write the objective function and all the constraints. b)…Ana is a university student with 12 hours available daily, and she wants to distribute her time betweenstudy (x) and leisure (y) activities. She wants to maximize her total enjoyment while fulfilling heruniversity obligations. Ana considers leisure to be twice (2) as enjoyable as studying, but she alsobelieves that she should spend at least twice (2) as much time studying as she does on leisure activities.Additionally, she cannot spend more than five (5) hours a day on leisure activities to ensure that she hasenough time for her university obligations. 1. How much additional enjoyment would Ana get if she had one more hour per dayavailable, so 13 instead of 12 (dual price)?2. Would Ana experience a greater level of enjoyment if she allows herself to have amaximum of six hours per day to leisure activities instead of five, while still fulfilling her universityobligations within the 12 hours available (dual price)?3. What is the allowable increase of the coefficient accompanying leisure…
- Explain all the steps when implementing the Branch and Bound method for the following optimization problem: Max 15*x1+12*x2+4*x3+2*x4 s.t. 8*x1+5*x2+3*x3+2*x4 <=10 3*x1+2*x3<=4 x1, x2, x3, x4 binaryThe Wearever Carpet Company manufactures two brands of carpet—shag and sculptured— in 100-yard lots. It requires 8 hours to produce one lot of shag carpet and 6 hours to produce one lot of sculptured carpet. The company has the following production goals, in prioritized order: (1) Do not underutilize production capacity, which is 480 hours. (2) Achieve product demand of 40 (100-yard) lots for shag and 50 (100-yard) lots for sculptured carpet. Meeting demand for shag is more important than meeting demand for sculptured, by a ratio of 5 to 2. (3) Limit production overtime to 20 hours. a. Formulate a goal programming model to determine the amount of shag and sculptured carpet to produce to best meet the company’s goals. b. Solve this model by using the computer.A travelling salesman, named Magan Shah plans to visit five cities 1, 2, 3, 4 and 5. The travel time (in hours) between these cities is shown below. To city 1 2 3 4 5 From city 1 x 5 8 4 5 2 5 x 7 4 5 3 8 7 x 8 6 4 4 4 8 x 8 5 5 5 6 8 x How should he schedule his touring plan in order to minimize the total travel time, if he visits each city once a week?