For each of the following two LP models, respond to the following questions using graphic tools and algebraic methods only: a) Identify the constraints that are binding and the ones that are not binding. b) Identify if any constraint is redundant (i.e., is not needed to delineate the feasibility region) c) Find the range of optimality of both of the objective function coefficients Model 1: Maximize f = 4x + 7y subject to the following constraints: x+2y≤7 5x+3y≤12 y≤3 x and y are non-negative
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- The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?Formulate decision variable, objective function, and constraints only. Eastborne Realty has $2 million available for the purchase of new rental property. After an initial screening, Eastborne reduced the investment alternatives to townhouses and apartment buildings. Each townhouse can be purchased for $282,000, and five are available. Each apartment building can be purchased for $400,000, and the developer will construct as many buildings as Eastborne wants to purchase. Eastborne’s property manager can devote up to 140 hours per month to these new properties; each townhouse is expected to require 4 hours per month, and each apartment building is expected to require 40 hours per month. The annual cash flow, after deducting mortgage payments and operating expenses, is estimated to be $10,000 per townhouse and $15,000 per apartment building. Eastborne’s owner would like to determine the number of townhouses and the number of apartment buildings to purchase to maximize annual cash flow.
- Q2. Solve the given LP problem on the right by (LP): Max Z = 2X1 + 4X2 %3D using The Graphical Solution Method. a) Find the optimal solution, determine the solution type. b) Find the optimality range for the changes in the objective coefficient c2. c) Find the feasibility range for the changes in the Right Hand Side (RHS) of one st. 3X1 + 2X2 < 12 Xị + 2X2 s 8 2X1 + X2 2 2 X1, X2 2 0 of the binding constraints.Ian Langella faces a decision how large his gasoline station should be. The annual returns wil l depend on both the size of his station and number of marketing factors related to the oil in dustry and demand for gasoline. Ian develop a careful analysis based on the following table: Size of first station Market condition Market conditon Market conditon Good Fair Poor Small 50,000 20,000 -10,000 Medium 80,000 30,000 -20,000 Large 100,000 30,000 -40,000 Very large 300,000 25,000 -160,000 Develop a decision table for this decisionWhat will be Hale’s TV Production’s decision based on the following criteria:a. MAXIMAXb. MAXIMINc. MINIMAX REGRETd. EXPECTED VALUEe. Construct the decision tree for this problem and indicate the decision based on the decision tree analysis.can you pls answer letter a,b,c
- GENERATE THE DECISION VARIABLE SOLUTION AND GENERATE AN ANSWER REPORT 3. The Wisham family lives on a farm in South Georgia on which it produces a variety of crops and livestock, including pecans. It has 5 acres of pecan trees that yield approximately 1,000 pounds of unshelled pecans per acre each year. The family uses all of its pecan harvest to produce pecan pies, cookies, 1-pound bags of shelled pecans, and 5-pound bags of unshelled pecans, which it sells in town at the local farmers' market. The family sells pies for $5, packages of a dozen cookies for $3, bags of shelled pecans for $7, and bags of unshelled pecans for $16. A shelled pecan is half the weight of an unshelled pecan. It requires 4 ounces of shelled pecans to make a pie, and 6 ounces of shelled pecans to make a dozen cookies. The pies and cookies are baked in the family oven, and there are 120 hours of baking time available. It takes 55 minutes to bake a batch of 4 pies and 15 minutes to bake a batch of 2 dozen…Ohio Swiss Milk Products manufactures and distributes icecream in Ohio, Kentucky, and West Virginia. The companywants to expand operations by locating another plant innorthern Ohio. The size of the new plant will be a function ofthe expected demand for ice cream within the area served bythe plant. A market survey is currently under way to deter-mine that demand.Ohio Swiss wants to estimate the relationship between themanufacturing cost per gallon and the number of gallonssold in a year to determine the demand for ice cream and,thus, the size of the new plant. The following data have beencollected:a. Develop a regression equation to forecast the cost per gal-lon as a function of the number of gallons produced. b. What are the correlation coefficient and the coefficient ofdetermination? Comment on your regression equation inlight of these measures.c. Suppose that the market survey indicates a demand of325,000 gallons in the Bucyrus, Ohio area. Estimate themanufacturing cost per gallon…A local real estate investor in Kingston is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the theater will be relatively stable under any conditions. The following payoff table shows the profit or loss that could result from each investment: Real Estate Investor Payoff Table Payoffs are Profits States of Nature (Gasoline Availability) Decision Alternatives Shortage Stable Supply Surplus Motel $–8,000 $15,000 $22,000 Restaurant $2,000 $8,000 $6,000 Theater $6,000 $6,000 $5,000 Which option should the real estate investor choose if he uses the LaPlace criterion? Using…
- Calculating outcomes as equally likely would BEST describe: O a. Maximax criterion O b. Laplace criterion O c. Regret criterion Od. Maximin criterion Determining the average payoff for each alternative and choosing the one with the BEST payoff is the approach called: ea, maximax O b. minimax regret O c. laplace Od maximin MHow to solve descision tree using Analytical Solver for the assignment below Chelsea Bush is an emerging candidate for her party’s nomination for president of the United States. She now is considering whether torun in the high-stakes Super Tuesday primaries. If she enters the Super Tuesday (ST) primaries, she and her advisers believe that she will either do well (finishfirst or second) or do poorly (finish third or worse) with probabilities 0.4 and 0.6, respectively. Doing well on Super Tuesday will net the candidate’s campaignapproximately $16 million in new contributions, whereas a poor showing will mean a loss of $10 million after numerous TV ads are paid for. Alternatively, shemay choose not to run at all on Super Tuesday and incur no costs.Chelsea’s advisors realize that her chances of success on Super Tuesday may be affected by the outcome of the smaller New Hampshire (NH) primary occurringthree weeks before Super Tuesday. Political analysts feel that the results of New…Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality