Data Modelling Assignment at my assignment hlep

Questions: (1) During their spare time in college, Anders and Michael have developed software to regulate traffic on internet sites. Their product is very original, and they have applied for a patent. They estimate that there is an 80% chance of their patent being approved.Last week, Anders and Michael have presented their ideas to Singular Inc., the dominant player in this market, after Singular had signed a confidentiality agreement with Anders and Michael. Yesterday, Singular announced a new software product that looks suspiciously similar to the software that Anders and Michael have developed. Anders suggested to sue Singular immediately, but Michael felt they should wait until they receive notification of their patent (which is still pending). Michael reasoned that their case will be much stronger if they had a patent on the product.Suppose that Anders and Michael have a 90% chance of winning a lawsuit against Singular if their patent is approved, and they have a 60% chance of winning a la wsuit while their patent is still pending. However, if their patent is not approved, then the chance of winning a lawsuit drops to 40%. In any case, Anders and Michael expect to win $1,000,000 if the lawsuit is successful. However, they estimate that suing Singular Inc. would cost $100,000, no matter whether the patent is still pending, approved or rejected.(a) Using a decision tree, decide what Anders and Michael should do to maximise the expected profits!(b) Singular informally makes a "now-or-never" offer to buy Anders' and Michael's software for $500,000. Should Anders and Michael agree to this offer?(2) The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages. The expected profit is $5/unit on special risk insurance and $2/unit on mortgages. Management wishes to establish sales quotas for the new product lines to maximise the total expected profit. The work requirements are as follows:(a) Formulate a linear program for this problem! Work-hours per unit Work-hours Department Special risk Mortgage available Underwriting 3 2 2,400 Administration 0 1 800 Claims 2 0 1,200 (b) Try to find sales quotas for the new product lines that satisfy the available work-hour limits and maximise the total expected profits You do not have to find the optimal quotas, but you should justify your choice of quotas! Answers: 1(a) Decision tree model The decision tree model is an extensive form of game representation in which the decision maker plays a game against the opponent called nature that randomly generates an outcome for chance variables that affect the eventual payoffs (Wu, 2011). In the following table for each option the possible outcomes and profit levels have been determined. Options Expected profit rates Probability Approval of patent 1,00,000 .90 Non approval of patent 1,00,000 .60 In the event Anders and Michael files a lawsuit they will either win or lose however they will incur an expense of around 1, 00,000 as lawsuit expenses (Fefferman, 2011). Hence if the software producers gets the approval then (100000 100000) = 0 Hence, the profit and the expenses being equal the software producers will not benefit from the win. Similarly, in case the approval is not granted the expected profit and the expense being 1, 00,000 the software developers will again suffer from loss. Expected profit with approval of patent = 1, 00,000 * 0.90 = 90000 Expected profit with non approval of patent = 1, 00,000 * 0.60 = 60000 Hence based on these two figures the software developers can take a decision before filling the law suitcase. Since the expected rate of profit is high in case the approval of the patent is received, hence it is advisable for the software developers to file the case after the approval of the patent is received. Otherwise, the chance of profit reduces and the lawsuit an expense has to be bore that will generate a loss for the software developers (Yang, 2008). 1(b) Evaluation of acceptance of offer given by Singular Inc The informal offer made by Singular Inc is not legally bound by any contract hence the acceptance of the offer may stand void at the time of payment. However, from the financial point of view the software company will benefit from the offer because the decision tree shows that the maximum that the software developers can get is around 90000 on getting an approval of the patent (Bazaraa, Jarvis Sherali, 2010). The now or never offer helps the software developers to get around 50000 which is high compared to the expected profit. The expected profit that the software developers are expecting to get is around 100000 with 90% probability of securing the patent approval. The law suit expenses will also amount to around 100000. Hence, even if the software developers secure the patent approval they area not able to maximize their profit. However with the now or never offer made by the company they would be able to secure 500000 without incurring in lawsuit expenses. Therefore, from the fina ncial point of view it is advisable for the software developers to accept the now or never offer given by the Singular Inc. This will help the software developers to get financial access and also reduce the expenses (Derhy, 2010). 2 (a) Linear program Formulation Objective function The objective formulation of a company is either to maximize profit or minimize cost. Here the objective function of the company is to maximize profit (Luenberger Ye, 2010). For this matter, the two variables Special risk insurance and mortgages are taken to be X1 and X2 respectively. The expected profit is $ 5 per unit on Special risk insurance $ 2 per unit on mortgages Special risk insurance (X1) 1 unit profit = 5 Or, X1 unit profit = 5X1 Mortgage 1 unit profit = 2 Or, X2 unit profit= 2X2 Therefore the total profit of both the variables Max Z = 5X1 + 2X2 Formulation of constraints The three different types of constraint conditions in this case are underwriting, administration and claims. Underwriting constraint 3X1 + 2X2 2400 Administration constraint 0X1 + 1X2 800 Claims constraint 2X1 + 0X2 1200 So the LPP problem looks like Max Z = 5X1 + 2X2 Subject to 3X1 + 2X2 24000 0X1 + 1X2 800 2X1 + 0X2 1200 And X1, X2 0 2(b) Sales forecast With the help of the LPP the following sales quotas can be forecasted: Target Cell (Max) Cell Name Original Value Final Value $B$5 Z X1 3600 3600 Adjustable Cells Cell Name Original Value Final Value $B$4 Solutions X1 600 600 $C$4 Solutions X2 300 300 Constraints Cell Name Cell Value Formula Status Slack $B$12 Constaint 1 LHS 2400 $B$12=$C$12 Binding 0 $B$13 Constaint 2 LHS 300 $B$13=$C$13 Not Binding 500 $B$14 Constaint 3 LHS 1200 $B$14=$C$14 Binding 0 So, it can be said that the organization needs to sales 600 units of Special risk insurance and 300 units of mortgages to earn maximum profits. Reference list Bazaraa, M., Jarvis, J., Sherali, H. (2010). Linear programming and network flows. Hoboken, N.J.: John Wiley Sons. Derhy, M. (2010). Linear programming, sensitivity analysis and related topics. New York: Prentice Hall. Fefferman, C. (2011). Interpolation by linear programming I. DCDS-A, 30(2), 477-492. doi:10.3934/dcds.2011.30.477 Luenberger, D., Ye, Y. (2010). Linear and nonlinear programming. New York: Springer. Wu, J. (2011). Linear Programming Solving the Optimization Question of Production Plan. AMR, 179-180, 1162-1166. doi:10.4028/www.scientific.net/amr.179-180.1162 Yang, X. (2008). Introduction to mathematical optimization. Cambridge, UK: Cambridge International Science Pub.