Posted: September 10th, 2023

The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages

2. The Primo Insurance Company is introducing two new product lines: special risk insurance and mortgages. The expected profit is £5 per unit on special risk insurance and £2 per unit on mortgages. Get research paper samples and course-specific study resources under   homework for you course hero writing service – Manage ment wishes to establish sales quotas for the new product lines to maximize total expected profit. The work requirements are as follows:

Work-Hours per Unit Work-Hours Available
Department Special Risk Mortgage
Underwriting 3 2 2,400
Administration 0 1 800
Claims 2 0 1,200

a. Formulate the decision problem as a LP.
b. Solve the LP using graphical solution method and interpret the obtained result.

3. Lemington’sis 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 of 400 and standard deviation of 100. The contract between Jean Hudson and Lemington’s works as follows. At the beginning of the season, Lemington’s reserves x units of capacity. Lemington’s 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 Lemington’s 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 Lemington’s orders 450 dresses and demand is for 400 dresses, Lemington’s will receive 400 dresses and owe Jean 400(£50) + 50(£5). How many units of capacity should Lemington’s reserve to maximise its expected profit?

a) Set up a simulation model to help the company make the decision of how many units of capacity to reserve.
b) Discuss on the obtained results and make suggestions. For example, what if the demand for the dress has different distributions?

4. The Ventron Engineering Company has just been awarded a £2 million development contract by the British Army Aviation Systems Command to develop a blade spar for its Heavy Lift Helicopter program. The blade spar is a metal tube that runs the length of and provides strength to the helicopter blade. Due to the unusual length and size of the Heavy Lift Helicopter blade, Ventron is unable to produce a single-piece blade spar of the required dimensions using existing extrusion equipment and material. The engineering department has prepared two alternatives for developing the blade spar: (1) sectioning or (2) an improved extrusion process. Ventron must decide which process to use. (Backing out of the contract at any point is not an option.) The risk report has been prepared by the engineering department. The information from this report is explained next. The sectioning option involves joining several shorter lengths of extruded metal into a blade spar of sufficient length. This work will require extensive testing and rework over a 12-month period at a total cost of £1.8 million. Although this process will definitely produce an adequate blade spar, it merely represents an extension of existing technology.
To improve the extrusion process, on the other hand, it will be necessary to perform two steps: (1) improve the material used, at a cost of £300,000, and (2) modify the extrusion press, at a cost of £960,000. The first step will require six months of work, and if this first step is successful, the second step will require another six months of work. If both steps are successful, the blade spar will be available at that time, that is, a year from now. The engineers estimate that the probabilities of succeeding in steps 1 and 2 are 0.9 and 0.75, respectively. However, if either step is unsuccessful (which will be known only in six months for step 1 and in a year for step 2), Ventron will have no alternative but to switch to the sectioning process and incur the sectioning cost on top of any costs already incurred. Development of the blade spar must be completed within 18 months to avoid holding up the rest of the contract. If necessary, the sectioning work can be done on an accelerated basis in a six-month period, but the cost of sectioning will then increase from £1.8 million to £2.4 million. The director of engineering, Dr. Smith, wants to try developing the improved extrusion process. He reasons that this is not only cheaper (if successful) for the current project, but its expected side benefits for future projects could be sizable. Although these side benefits are difficult to gauge, Dr. Smith’s best guess is an additional £2 million. (These side benefits are obtained only if both steps of the modified extrusion process are completed successfully.)
a) Construct a decision tree for this problem.
b) How much would Ventron be willing to pay, right now, for perfect information about both steps of the improved extrusion process?

5. The file ‘House Sales.xlsx’ contains monthly data on the number of new one-family houses sold in the United States (in thousands) from January 1991 through June 2015 – Research Paper Writing Help Service. (These data, available from the U.S. Census Bureau website, are listed as SAAR, seasonally adjusted at an annual rate.) Housing sales were steadily trending upward until about the beginning of 2006 – Write a paper; Professional research paper writing service – Best essay writers, then the bottom fell out of the housing market, and sales eventually started trending upward again.
a) How well does simple exponential smoothing with α=0.3 work with this data set?
b) What smoothing constant should be used?

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