Suppose that the government charges a toll t (a congestion charge) for each journey. Find the optimum toll. Interpret your answer in terms of the externality that each driver imposes on others.
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Question 2
A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N ) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by
c(N) = a+bN,
for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once.
the number of drivers that join the road is Ne = (v−a)/b
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(iv) Suppose that the government charges a toll t (a congestion charge) for each journey. Find the optimum toll. Interpret your answer in terms of the externality that each driver imposes on others.
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- Question 4Consider a birth death model with birth rates in states n = 0, 1, . . . and death rates in states n = 1, 2, . . (a) Give the detailed balance conditions for the equilibrium probability of being in state n, for n = 0, 1, . . . and explain how they are derived. (b) Using the detailed balance conditions derive an expression and state any condition needed to ensure that the equilibrium distribution exists. (c) i Now consider the M/M/1 queue with arrival rate λ and service rate µ and explain how it can be modelled as a birth death model. ii. For the M/M/1 queue derive the form of , the equilibrium distribution of the number of customers present, and give any conditions needed to ensure the existence of the equilibrium distribution. Derive the mean value of the equilibrium distributionQuestion content area Part 1 Phillip Witt, president of Witt Input Devices, wishes to create a portfolio of local suppliers for his new line of keyboards. As the suppliers all reside in a location prone to hurricanes, tornadoes, flooding, and earthquakes, Phillip believes that the probability in any year of a "super-event" that might shut down all suppliers at the same time at least 2 weeks is 3%. Such a total shutdown would cost the company approximately $480,000. He estimates the "unique-event" risk for any of the suppliers to be 5%. Assuming that the marginal cost of managing an additional supplier is $14,800 per year, how many suppliers should Witt Input Devices use? Assume that up to three nearly identical local suppliers are available. Part 2 Find the EMV for alternatives using 1, 2, or 3 suppliers. EMV(1)=$________ (Enter your response rounded to the nearest whole number.) Part 3 EMV(2)=$________ (Enter your response rounded to the nearest whole…Question A firm that assembles refrigerators and stoves is about to start production of new models of each. Each model will require assembly time, inspection time, and storage space. The amounts of each of these resources that can be devoted to the production of the items is limited. The manager of the firm would like to determine the quantity of each item to produce in order to maximize the profit generated by sales. He has the following data at his disposal: Refridgerators Stoves Profit per unit $60 $50 Assembly time per unit 4 hours 10 hours Inspection time per unit 2 hours 1 hour Storage space per unit 3 cubic feet 3 cubic feet Other information Resource Amount of time available Assembly time 100 hours Inspection time 22 hours Storage space 39 cubic feet Questions - •Identify the feasible solution space. •At which point will profit be maximized?
- Question 2: Sunblessed Juice Company sells bags of oranges and cartons of orange juice. Sunblessed grades oranges on a scale of 1 (poor) to 10 (excellent). At present, Sunblessed has 220,000 pounds of grade 6 oranges and 150,000 pounds of grade 9 oranges on hand. The average quality of oranges sold in bags must be at least 7, and the average quality of oranges used to produce orange juice must be at least 8. Each pound of oranges that is used for juice yields a revenue of $2.25 and incurs a variable cost (consisting of labor costs, variable overhead costs, inventory costs and so on) of $1.35. Each pound of oranges sold in bags yields a revenue of $2.00 and incurs a variable cost of $1.20. Determine how Sunblessed can maximize its profit. Please include your answer report with the model, and a description of your recommendation. Use SolverTable to determine how a change in the cost per bag of oranges changes the optimal solution. Specifically, vary the cost from $1.00 to $1.50 in…Which of the following is not true? Question 6 options: 1) Climate involves statistics (e.g., long-term averages) but weather considers conditions at a particular time and place (e.g., one week of this summer). 2) The current weather at a location can be characterized by a single measurement, but climate requires many years of measurements (typically around 30) to characterize. 3) Both weather and climate can vary regionally (e.g., from one side of a mountain range to another). 4) Climate only refers to temperatures, but weather also includes other factors like wind, rain, and snow.Question 1 B A company produces 2 (two) different grades of gasoline – regular and premium from 3(three) components (1,2,3). The company wants to determine the optimal mix of the three components in each grade of the gasoline that will maximize profit. The maximum quantities available for each component and their cost per gallon are as follows:Component Cost per gallon maximum gallons available per day 1 2.50 5,000 2 2.60 10,000 3 2.84 10,000 In order to ensure the appropriate blend, each grade has certain specifications as follows: Grade Component Specs Selling Price per gallon Regular At most 30% component 1 At least 40% component 2 At most 20% component 3 2.90 Premium At least 25% component 1 At most 45% component 2 At Least 30% component 3 3.00 The company wants to produce at least 10,000 gallons of each grade of gasoline. Formulate a LP model including the ratio constraints, production constraints and the objective function for this question.
- Question 1. Busch Gardens Sweets is preparing for the Halloween rush. They prepare two sizes of Peanut/Raisin Ghoulish Delight and need to calculate how many bags of deluxe and standard mixes they can produce. • The deluxe mix takes 0.9 of a pound of raisins and 0.4 of a pound of peanuts.• The standard mix takes 0.7 of a pound of raisins and 0.6 of a pound of peanuts.The shop has 100 pounds of raisins and 70 pounds of peanuts. The profit on the deluxe mix is $1.80 and the standard mix profit is $1.60. The owner wants no more than 110 bags of each type prepared. Do not forget the non-negativity constraint and remember that you cannot sell partial bags (whole numbers only). Use Excel Solver Question 2. Take a screenshot (snip tool) of you excel spreadsheet and save it.Question 3 A research collaboration can be enhanced by: Limiting the communication between researchers and industry partners. Avoiding the issue of which journal to target since research team members might disagree. Discussing intellectual property issues while the collaboration is forming. Waiting to discuss authorship issues until after data collection. Question 4 In any collaboration, data ownership is typically determined by: The research team with access to the best lawyers. The individual who does the most work on the project. The type and source of funds used to support the project. The relevant department chairs.*Question on LP*A company produces two products that are processed on two assembly lines. Assembly line one has 100 available hours and assembly two has 42 available hours. Each product requires 10 hours of processing time in assemble line one. Whilst on assemble line two, product one requires 7 hours and product two 3 hours. The profit for product one is ghc 6 per unit. The profit for product two is ghc 4 per unit. Management wishes to know how many units of each product to produce in order to maximize total profit. a) Define the decision variables for this Linear Programming problem b) Formulate a LP model for this problem c) Solve this model using graphical analysis.
- Question: You want to buy electric energy. You can buy from company A, B, C, or D, but you must choose only one. You obtain past data on these four suppliers, and you then determine that the prices for some of them have been quite volatile, influenced by the state of the economy (recession, stagnation, and inflation). You assess this data given in the table in the picture attached. a) Assuming that you simply want to minimize your average costs over the long run, determine the expected costs for all energy suppliers. Select the supplier based on minimum expected cost. b) Assuming that you cannot afford any surprises and therefore want to minimize his uncertainty, determine the standard deviation for each supplier. Select the supplier based on minimum variance (same as minimum standard deviation).dent question I am having trouble formulating the objective function and constraints. Jeremy Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder rods is $1800 and the cost required to set up the production line for the 6-cylinder rods is $3200. Manufacturing costs are $16 for each 4-cylinder connecting rod and $20 for each 6-cylinder connecting rod. The production capacities are 5800 and 7200 for 6 and 4 cylinder rods respectively. The operating budget is $100,000. The selling prices are $55 per 4-cylinder rod and $70 per 6-cylinder rod. What is the optimal number of 4 and 6 cylinder rods that should be produced by the company? Identify the type of integer programming framework (Total Integer, Mixed Integer or Binary) that applies to this problem, develop the appropriate formulation (decision variables, objective function and constraints)QUESTION 2 Samy Company manufactures two types of tables, model K and J. The production of a model K table requires a capital expenditure of RM 6 and 2 hours of labor. The production of a model J table requires a capital of RM 4 and 5 hours of labor. The company has RM 240 capital and 100 hours of labor available for the production of the two models of tables per week. A model K table contributes a profit of RM 30 while model J contributes RM 40. a. Formulate the problem using linear programming model. b. How many of each type of table should the firm produce to maximize the profit? c. What is the maximum profit?
