Quantative analysis for business

Establishing random number intervals for each of the three variables iv. Generating random numbers v. Simulating a series of trials – in this case ten (10) trials will be simulated Step 1 and 2 – Probability and cumulative probability distribution Materials: Cost ($) Probability Cumulative probability 33 0.18 0.18 35 0.23 0.41 38 0.32 0.73 39 0.27 1.00 Table 1.1 Labor: Cost ($) Probability Cumulative probability 22 0.12 0.12 23 0.18 0.30 24 0.22 0.52 25 0.28 0.80 28 0.20 1.00 Table 1.2 Utilities: Cost ($) Probability Cumulative probability 3 0.26 0.26 4 0.43 0.69 6 0.31 1.00 Table 1.3 Steps 1 and 2 are merged in order to provide a clear picture of how the cumulative figures were arrived at. The probabilities are given and the cumulative probabilities are the cumulative totals of these probabilities as shown in Table 1.1 to Table 1.3 Step 3 Determine Random Number Intervals Materials: Cost ($) Cumulative probability Interval of Probability Random Numbers 33 0.18 0.18 01 – 18 35 0.41 0.23 19 – 41 38 0.73 0.42 42 – 73 39 1.00 0.27 74 – 1.00 Table 1.4 Labor: Cost ($) Cumulative probability Interval of Probability Random Numbers 22 0.12 0.12 01 – 12 23 0.30 0.18 13 – 30 24 0.52 0.22 31 – 52 25 0.80 0.28 53 – 80 28 1.00 0.20 81 – 00 Table 1.5 Utilities: Cost ($) Cumulative probability Interval of Probability Random Numbers 3 0.26 0.26 01 – 26 4 0.69 0.43 27 – 69 6 1.00 0.31 70 – 00 Table 1.6 The random numbers relating to the relevant costs associated with the three variables were determined Steps 4 and 5 - Generating random numbers and simulating a series of trials Monte Carlo Simulation Results Materials Labor Utilities Total Random Cost Random Cost Random Cost Cost Trial Number per Unit Number per Unit Number per Unit per Unit 1 28 35 21 23 85 6 64 2 14 33 50 24 64 4 61 3 44 38 90 28 15 3 69 4 51 38 71 25 66 4 67 5 91 39 10 22 45 4 65 6 38 35 11 22 74 6 63 7 79 39 70 25 62 4 68 8 70 38 16 23 18 3 64 9 98 39 88 28 74 6 73 10 11 33 67 25 35 4 62 Total 367 245 44 656 Average 36.7 24.5 4.4 65.6 Table 1.7 Steps 4 and 5 have also been merged. The random numbers were taken from a random number table and the relevant material cost that falls within the corresponding random number interval in Step 3 were written beside them. The information in Table 1 indicates the following: 1. The average material cost per unit is $36.70 2. The average labor cost per unit is $24.50 3. The average utilities cost per unit is $4.40 4. The average total cost per unit is $65.60 Part B The selling price that should be established, assuming the company wants an average markup of $20 on each unit sold is calculated as follows. $ Average total cost 65.60 Add: Markup 20.00 85.60 The results of the calculations indicate that in order to obtain an average markup on the cost of the product the company has to sell it for an average price of $85.60. Inventory Management Part A The amount of inventory that Company A needs to order can be determined with the use of economic order quantity (EOQ) model. According to Williamson (2012) EOQ models are used for identifying the optimal order quantity. In order to do this the model minimizes the sum of certain costs that vary with order size and the frequency of orders. Williamson (2012) describes three order size models – the basic economic order quantity (EOQ) model; the economic production quantity (EPQ) model; and the quantity
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