Please use graphic tools and algebra methods to answer this question For each of the following two LP models, respond to the following questions using graphic toolsand 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 feasibilityregion)c) Find the range of optimality of both of the objective function coefficientsModel 1:Maximize f = 4x + 7y subject to the following constraints:x+2y≤75x+3y<12y≤3x and y are non-negative

Objective Functions and Constraints: Based on the given details, the objective…

Answered: For each of the following two LP…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 35P

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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?
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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…
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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 M
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Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality

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