Four qualified postgraduate students are to be allocated to four professors. The preferencegiven by student (scale 1-10) is shown as table below.StudentAВCDProfessorJamesJordanJanet786.Jessy58.7(a) Formulate a linear programming model for the problem.[NOTE: Please use x,where i = 1, 2,...,n -Professor and j=1, 2,...,m -Student torepresent your decision variables.](b) From the output below, what is the optimal allocation plan and what is the totalpreference scales obtained from the allocation plan?Model Variable Original ValueFinal ValueValue x1111Value x121Value x131Value x14Value x21Value x22Value x2311111Value x241Value x31Value x32Value x331111Value x341Value x411Value x421Value x431Value x4411699445

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Answered: Four qualified postgraduate students…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 68P

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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.
Please show how to solve b
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CAN YOU EXPLAIN THREE OUTPUTS OF MARTRIX MODEL CONNNNUNICATION WITH SOME EXAMPLES?
Consider Bruno who manages an underwriting team in an insurance firm. Recently, the management of Bruno’s firm informed him of their decision to create a new risk assessment team, consisting of data scientists with machine learning expertise, and reduce the size of Bruno’s underwriting team. Bruno’s underwriting team will now work with the new risk assessment team in order to determine whether to provide insurance to applicants Use the model of a firm’s technology choice and graphically illustrate the management’s restructuring decision in a diagram with isocost curves. Your diagram should have the amount of human intelligence on the horizontal axis and the amount of artificial intelligence on the vertical axis. Fully label your diagram. Note that there are no actual numbers given in this question: you may make them up or simply use appropriate notations. Briefly explain the key information of your diagram.
(d) A company has three factories. Each factory produces three different products (A, B and C). Factory 1 has a daily production capacity production of 8 units of A, 4 units of B and 8 units of C. Factory 2 has a daily production capacity of 6 units of A, 6 units of B and 3 units of C. Factory 3 has a production capacity of 12 units of A, 4 units of B and 8 units of C. The total demand for product A is 300 units, for product B is 172 units and for product C is 250 units. The daily operating cost for Factory 1 is $55 for Factory 2 is $60 and for Factory 3 is $50. How many days should each factory be operated in order to fill the total demand and the keep the operating cost at a minimum? (iv) (v) Identify the entering, departıng and pivot variables. Use the simplex method to determine the optimal tableau. Ensure that you explain each step in the computation. Identify the basic and non-basic variables. (vii) Identify the optimal solution. (vi)
(d) A company has three factories. Each factory produces three different products (A, B and C). Factory 1 has a daily production capacity production of 8 units of A, 4 units of B and 8 units of C. Factory 2 has a daily production capacity of 6 units of A, 6 units of B and 3 units of C. Factory 3 has a production capacity of 12 units of A, 4 units of B and 8 units of C. The total demand for product A is 300 units, for product B is 172 units and for product C is 250 units. The daily operating cost for Factory 1 is $55 for Factory 2 is $60 and for Factory 3 How many days should each factory be operated in order to fill the total demand and the keep the operating cost at a minimum? (i) (ii) (iii) $50. Show a model that represents the company's problem. Write down the dual maximization problem. Write down the initial simplex tableau.

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