GEST 1013 Mathematics in Modern Society Topic 2: Decision Making Assignment 2 Question 1 (Relevant Costing) Mr. A has been asked to quote a price for a one-off contract. The following information is available: Materials The contract requires 3000 kg of material K, which is a material used regularly by the company in other production. The company has 2000 kg of material K currently in stock which had been purchased last month for a total cost of $19600. Since then the price per kilogram for material K has increased by 5%. The contract also requires 200 kg of material L. There are 250 kg of material L in stock which are not required for normal production. The material originally cost a total of $3125. If not used on this contract, the stock of material L would be sold for $11 per kg. Labour The contract requires 800 hours of skilled labour. Skilled labour is paid $9.5 per hour. There is a shortage of skilled labour and all the available skilled labour is fully employed in the company in the manufacture of product P. The following information relates to product P: S per unit $ per unit Selling Price 100 Less: Skilled Labour Other Variable Costs Contribution Required: Prepare on a relevant cost basis, the lowest cost estimate that could be used as the basis for a quotation. Question 2 (Make or buy decision) Company B makes four components W, X, Y and Z for which costs in the forthcoming year are expected to be as follows: W 1 1000 X 2000 Y 4000 Z Production (units) Unit Marginal Costs: Direct Materials Direct Labour Variable Production Overheads 5 9 Directly attributable fixed costs per annum and committed fixed costs: Incurred as a direct consequence of making W 1000 Incurred as a direct consequence of making X 5000 Incurred as a direct consequence of making Y 6000 Incurred as a direct consequence of making Z 8000 Other fixed costs (committed) 30000 50000 A sub-contractor has offered to supply units of W, X, Y and Z for $12, $21, $10 and $14 respectively. Required: Should Company B make or buy the components? Please explain. Question 3 (Outsourcing) Company C is considering a proposal to use the services of a press cuttings agency. At the moment, press cuttings are collected by a junior member of the marketing department, who is also responsible for office administration (including filling), travel bookings, a small amount of proof reading and making the tea. The total annual cost of employing this person is $15000 per annum. There is concern that the ability of this person to produce a comprehensive file of cuttings is limited by the time available. She has calculated that she needs to spend about two hours of her seven and a half hour day simply reading the national and trade press, but usually only has about five hours a week for this job. Press subscriptions currently costs $850 per annum and are paid annually in advance. The assistant makes use of a small micro-fiche device for storing cuttings. The cuttings are sent to a specialist firm once a month to be put into fiche. Company C pays $45 each month for this service. The micro-fiche reader is leased at a cost of $76 per calendar month. This lease has another 27 months to run. The cutting service bureau has proposed an annual contract at a cost of $1250. Several existing users has confirmed their satisfaction with the service they receive. Required: Should Company Coutsource its press cuttings work? Please explain. Question 4 (Further Processing) Company D manufactures four products from an input of a raw material to Process 1. Following this process, product U is processed in Process 2, product V in Process 3, product Win Process 4 and product X in Process 5. The normal loss in Process 1 is 10% of input, and there are no expected losses Process 1 are apportioned to each product according to the volume of output of each product. Production overhead is absorbed as a percentage of direct wages. Data in respect of a particular month Process Total 1 2 3 4 5 $'000 $000 $'000 $000 $000 $'000 Direct Material at $1.25 100 100 per litre Direct Wages 48 12 8 4 16 88 Production Overhead 66 W Product V litres litres 20000 10000 litres 22000 litres 18000 Output or Selling Price Estimated Sales Value at end of Process 1 2.5 Required: Suggest and evaluate an alternative production strategy which would optimize profit for the month. It should not be assumed that the output of Process 1 can be changed. Question 5 (Shut down decisions) Company E manufactures three products X, Y and Z. The present net annual income from these is as follows: Y Total $'000 $'000 $'000 $'000 Sales 40 150 Variable Costs Contribution Fixed Costs Profit/(Loss) 50 20 15 Company E is concerned about its poor profit performance, and is considering whether or not to cease selling Y. It is felt that selling prices cannot be raised or lowered without adversely affecting net income. $5000 of the fixed costs of Y are direct fixed costs which would be saved if production ceased (that is, there are some attributable fixed costs). All other fixed costs, it is considered, would remain the same. By stopping production of Y, it were possible to use the resources realized for the production of a new item U. U, which would sell for $50000 and incur variable costs of $30000 and extra direct fixed costs of $6000. Required: Suggest whether Company E should shut down the production of Y and switch resources to make U. Please explain. Question 6 (Expected Values) Mr. F has to choose between mutually exclusive options A and B, and the probable outcomes of each option are as follows: Option A Profit/(Loss) Probability 0.8 5000 0.2 6000 Option B Profit/(Loss) Probability 0.1 0.2 (2000) 5000 7000 8000 0.6 0.1 Required: Based on expected values, which option is the best? Question 7 (Probability Distribution) Mr. G has to choose between mutually exclusive options C and D and the possible outcomes of each option are as follows: Option Cost Probability 0.29 0.54 0.17 15000 20000 30000 Option D Cost Probability 0.03 0.3 0.35 0.32 14000 17000 21000 24000 Both options will produce an income of $30000. Required: Which option should be chosen? Please explain. Question 8 (Decision Rules) Mr. H is considering which one of three alternative courses of action A, B and C to take. The profit or loss from each choice depends on which one of four circumstances, I, II, III or IV will apply. The possible profits and losses, in thousands of dollars, are given in the following payoff table. Losses are shown as negative figures: Action A Action C Action B 60 -10 Circumstance I Circumstance II Circumstance III Circumstance IV 80 50 115 60 100 Required: State which action would be selected using each of the decision rules: maximax, maximin and minimax regret criteria Question 9 (Decision Rules) Suppose the budgeted demand for product X will be 11500 units if the price $10, 8500 units if the price is $12 and 5000 units if the price is $14. Variable costs are estimated at either $4, 55, or $6 per unit. A decision needs to be made on the price to be charged. Here is a contribution table showing the budgeted contribution for each of the nine possible outcomes: Demand Price Variable Cost Unit Total Contribution Contribution 11500 11500 8500 8500 8500 5000 5000 5000 69000 57500 46000 68000 59500 51000 50000 45000 40000 Required: State which price should be set using each of the decision rules: maximax, maximin and minimax regret criteria Question 10 (Decision Tree) A firm has developed a new product X. They can either test the market or abandon the product. The details are set out below: Test market cost $50000; likely outcomes are favourable (probability = 0.7) or failure (probability = 0.3). If favourable they could either abandon or produce it when demand is anticipated to be: Low Demand Probability = 0.25 Loss $100000 Medium Demand Probability = 0.6 Profit $150000 High Demand Probability = 0.15 Profit $450000 If the test market indicates failure the project would be abandoned. Abandonment at any stage results in a gain of $30000 from the special machinery used. Required: Draw the decision tree showing the possible cases with probabilities GEST 1013 Mathematics in Modern Society Topic 3: Linear Correlation and Regression Analysis Assignment 3 Question 1 For the following data: Required: Draw a scatter diagram. (b) Find an equation of the line of best fit. Estimate a value of y corresponding to x = 10 Question 2 As part of an investigation into levels of overtime working, a company decides to tabulate the number of orders received weekly and compare this with the total weekly overtime worked to give the following: 2 3 4 5 6 8 9 10 7 135 22 107 55 48 92 32 67 122 Week 1 Number Orders 83 received Total 38 Overtime Hours 9 42 18 30 48 10 29 Required: Find an equation of the line of best fit. Estimate total overtime hours necessary for 100 orders. Given that normal weekly hours for an employee are currently 35, state in words what criterion is necessary for the company to consider taking on a new employee. Question 3 The following data relate to length of public roads in '000 km) and number of goods vehicles with current licenses (in '000) for eight successive years:: 318 320 322 325 327 329 331 Length 316 of roads Number 1692 of licenses 1640 1640 1630 1632 1660 1736 1778 Required: Find the coefficient of linear correlation. Question 4 On ten different days (picked at random) the following values were obtained for the price of a share for a particular company together with the value of FTSE (Financial Times Stock Exchange) Index on that day: 77 4680 76 65 7160 75 76 Share Price (in pence) FTSE Index 319 315387339383 340 340 356 358 398 Required: Find Spearman's rank correlation coefficient and say whether FTSE Index is a reasonable indicator for the price of the company's share. Question 5 As an exercise, a company asked its Stores Supervisor and Purchase Manager to independently rank its eight main suppliers (A, B, C, D, E, F, G and H) in order to value to the company, taking into account such factors as reliability, volume, special discounts and product quality. The two managers ranked the suppliers in order of preference as follows: C G Stores Supervisor Purchase Manager DT Required: Find Spearman's rank correlation coefficient to determine the amount of agreement between the two. Can any conclusions be drawn about the suppliers