...espondence concerning this article should be addressed xxxxxx, care of Western Governors University. E-mail: xxxxx@wgu.edu QAT1 Task 2: Competency 309.3.1-03, 11, 12 Determine the equations for each of the three constraints. Nutrient C : 4x + 4y ≤ 30 Flavor A : 12x + 6y ≤ 72 Color : 6x + 15y ≤ 90 Identify each constraint as Minimum or Maximum. Nutrient C constraint is a Maximum Flavor A constraint is a Maximum Color is a Maximum Determine the total contribution to profit that lies on the Object Function as plotted on the graph. By visual observation the objective function line indicates shows Brand X = 3 and Brand Y = 4. Using these values and the objective function of 30y + 40x = 30*4 +40*3 = 240 Determine how many cases of each type should be produced to generate the greatest profit. Solving for the intersection of Color (4x + 4y = 30) and Nutrient (6x + 15y = 90) yields the values of Y = 5 case and X = 2.5 cases for a total of 7.5 Cases. Entering these values into the objective function: 30y + 40x = 30*5 + 40*2.5 = 250 Solving for the intersection of Flavor (12x + 6y = 72) and Color (4x + 4y = 30) yields the values of Y = 3 and X = 4.5 cases for a total of 7.5 cases. Entering these values into the objective function: 30y + 40x = 30*3 + 40*4.5 = 270 Solving for the intersection Flavor (12x + 6y = 72) and Nutrient (6x + 15y = 90) yields the values of Y = 4.5 and X =3.75 for a total of 8.25 cases. Entering these values into the objective function: ...
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...A) a) Color Additive is constrained to a maximum of 90 units per each production period. 6x + 15y is less than or equal to 90. The constraint equation is y=6-0.4x. This is a maximum constraint. b) Flavor Additive is constrained to a maximum of 72 units per each production period. 12x + 6y is less than or equal to 72. The constraint equation is y=6-0.5x. This is a maximum constraint. c) Nutrient C is constrained to a maximum of 30 units per production period. 4x + 4y is less than or equal to 30. The constraint equation is y=7.5-1x. This is a maximum constraint. B) If the company produces a combination of cases of Brand X and Brand Y the total contribution of profit that lies on the objective function is: (P) = ($40*6) + ($30*0) = $240. C) The cases of Brand X and Brand Y that I recommend should be produced during each production period for optimum production if Company A wants to generate the greatest amount of profit are: Using the provided graph, I slid the profit line out as far as possible, while maintaining the same slope, until it reached the very edge of the feasible region bounded by the three constraints. I then plugged the coordinates into the profit equation from B (shown below): Origin (x 0, y 0) 0 cases of Brand X (x=0), 0 cases of Brand Y (y=0): P = (40*0) + (30*0) = $0 Point 1 (x 0, y 6) 0 cases of Brand X (x=0), 6 cases of Brand Y (y=6): P = (40*0) + (30*6) = $180 Point 2 (x 2.5, y 5) 2.5 cases of Brand...
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...Company A: Demand (D) = 400,000 units per year Q = sqrt((2*400,000*42)/42) = 238000 = 894.43 Ordering Costs (Co) = $42 per order Per Unit Cost of inventory =500 Holding cost rate = 3% Holding cost(Ch) = $500(.03) = $15.00 Q = 894 To find the order size for Company A in the scenario above that would minimize total annual cost I chose to use the economic order quantity formula. The numbers for demand, ordering cost, holding cost and unit cost were given in the scenario. With this I determined the holding cost-per unit cost of inventory X holding cost rate=holding cost ---> 500x.03=$15 Once I had this number I inputed everything into the formula for economic order quantity, took the square root and got an order size of 894. With this information Company A TASK B: Company B: Demand (D) = 88,400,000 units per year Q=sqrt(2x(88,400,400x500)/10x(1-88,400,000/5,200,000))=23505.32 Production (P) = 5,200,000 units per year Production Setup Cost (Co) = $500 per order Per Unit Cost of inventory = $250 Holding cost rate = 4% Holding cost(Ch) = $250(.04) = $10.00 Q=23505 To find the lot size for Company B in the scenario above that would minimize total annual cost I chose to use the economic production lot model. The numbers for demand, production set up cost, holding cost and unit cost were given in the scenario. With this I determined the holding cost-per unit cost of inventory X holding cost rate=holding cost ---> 250x.04=$10 Once I had this number...
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...Expected Value of The Developing Theory To solve the expected Value you will multiply probablilty times the payoff DEVELOP THOROUGHLY Good~ 500000*.50= 250000 Expected Value of The Developing Theory Moderate~ 25000*.037=9250 Expected Value of The Developing Theory Poor~ 1000*.13=130 Expected Value of The Developing Theory DEVELOP RAPIDLY Good~ 500000*0.86=430000 Expected Value of The Developing Rapidly Moderate~ 25000*0.12=20 Expected Value of The Developing Rapidly Poor~ 1000*.0.02=20 Expected Value of The Developing Rapidly STRENGTHEN PRODUCTS Good~ 2000*.77=1540 Expected Value of Strengthening Products Moderate~ 10000*.06=600 Expected Value of Strengthening Products Poor~ 3000*.17=510 Expected Value of Strengthening Products REAP WITHOUT INVESTING Good~ 10000*.66=6600 Expected Value of Reap without investing Poor~ 1000*.34=340 Expected Value of Reap without investing Branch #1: Develop Thouroughly .50(50000) + .037(25000)+ .13(1000) = 250000 + 9250 + 130 = $259,380 Branch #2 Develop Rapidly .86(500000) + .12(25000) + .02(1000) = 430000 + 3000 + 20= $433,020 When looking at Developing New Product you would chose the alternative that...
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...QAT1 Task 5 Revised Task A. Develop New Product 1.) Develop Thoroughly= $210,200 2.) Develop Rapidly= $55,700 Consolidate Existing Product 3.) Strengthen Products= $64,900 4.) Reap Without Investing= $6,400 Task B. The decision alternative is to develop new products thoroughly, or decision alternative 1, with the expected value (EV) of $210, 200. 1. Decision alternative 1 has the highest expected value ($210,200) of all four branches, thus making it the most favorable decision. To find expected values for each decision alternative, first you multiply the Predicted Gains (or, Payoffs) by the Probability for each States of Nature (in this case, Market Reactions: Good, Moderate, and Poor). Then, you add the totals of each Market Reaction and that becomes the expected value for each decision alternative. The highest expected value from all the decisions is generally the most favorable decision. The following are the calculations for the expected values of each of the four decision alternatives: The formula is: EV= Predicted Gains(Probability) Decision alternative 1: Good: 500,000(.4) = 200,000 Moderate: 25,000(.4) = 10,000 Poor: 1,000(.2) = 200 Total: $210,200 Decision alternative 2: Good: 500,000(.1) = 50,000 Moderate: 25,000(.2) = 5,000 Poor: 1,000(.7) = 700 Total: $55,700 Decision alternative 3: Good: 200,000(.3) = 60,000 Moderate: 10,000(.4) = 4,000 Poor: 3,000(.3) = 900 Total: $64,900 Decision...
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...A1 a-d A1a A1b A1c A1d Trial Random # Materials Cost Per Unit Trial Random # Labor Cost Per Unit Trial Random # Utilities Cost Per Unit Total Cost Per Unit 1 74 $38.00 1 2 $22.00 1 5 $3.00 $63.00 2 57 $38.00 2 77 $28.00 2 42 $4.00 $70.00 3 67 $38.00 3 15 $22.00 3 65 $6.00 $66.00 4 41 $35.00 4 31 $24.00 4 75 $6.00 $65.00 5 28 $35.00 5 44 $24.00 5 65 $6.00 $65.00 6 75 $38.00 6 87 $28.00 6 95 $6.00 $72.00 7 35 $35.00 7 90 $28.00 7 48 $4.00 $67.00 8 79 $38.00 8 34 $24.00 8 13 $3.00 $65.00 9 10 $33.00 9 80 $28.00 9 67 $6.00 $67.00 10 95 $39.00 10 88 $28.00 10 10 $3.00 $70.00 11 39 $35.00 11 11 $22.00 11 99 $6.00 $63.00 12 27 $35.00 12 43 $24.00 12 97 $6.00 $65.00 Total $437.00 Total $302.00 Total $59.00 $798.00 Average $36.42 Average $25.17 Average $4.92 $66.50 A2. Materials Labor Utilities Cost Probability Cummulative Probability Cost Probability Cummulative Probability Cost Probability Cummulative Probability $33 0.20 0.00-0.20 $22.00 0.18 0.00-0.18 $3.00 0.16 0.00-0.16 $35 0.33 0.20-0.53 $23.00 0.08 0.18-0.26 $4.00 0.37 0.16-0.53 $38 0.37 0.53-0.90 $24.00 0.25 0.26-0.51 $6.00 0.47 0.53-1.00 $39 0.10 0.90-1.00...
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...Quantitative Analysis for Business (QAT1) Submitted 05/05/2015 Assignment 309.3.3-04 Version LMF5-28 Student: Richard McClanahan Student ID: 000343792 TASK #5 Answer Task 5A Calculate the expected value for EACH of the four decision branches. 1. Develop Thoroughly: GOOD) $500,000 (0.45) = $225,000 MOD.) $25,000 (0.10) = $2,500 POOR) $1,000 (0.45) = $450 TOTAL EXPECTED VALUE: $227,950 2. Develop Rapidly: GOOD) $500,000 (0.52) = $260,000 MOD) $25,000 (0.23) =$5,700 POOR) $1,000 (0.25) =$250 TOTAL EXPECTED VALUE: $265,950 3. Strengthen Products GOOD) $2,000 (0.33) = $660 MOD) $10,000 (0.52) = $5,200 POOR) $3,000 (0.15) = $450 TOTAL EXPECTED VALUE: $6,310 4. Reap without investing GOOD) $10,000 (0.33) = $3,300 POOR) $1,000 (0.67) = $670 TOTAL EXPECTED VALUE: $3,970 EXPLINATION: We take the projected payoff and multiply that payoff by the probability factor. So if the good payoff to develop a product rapidly is $500,000, we then multiply that by the probability factor of 52%, or 0.52. That gives us a probable payoff of $260,000. Following this simply process, we extrapolate these results as listed above. ANSWER TASK 5B After calculating the total expected value for each decision alternative, the most profitable decision would be to RAPIDLY DEVELOP new products for a probable...
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...EST 1-320.2.3-08 Lisa Jeffries 000238303 Code of Ethics In the outline below, I have listed some of the company’s codes of ethics. The company has the obligation to enforce the code of ethics, procedures, training, and to set up meetings for the employees and employer to discuss better ways of serving clients and providing a safer environment for employees. Mission statement: To be the leading systems, services and solutions provider in the world by exceeding customers' expectations through superior service delivery, world-class talent and applied technological innovation, making this the most profitable business s company. The company makes the customer service experience the "Best in Class". Maximize shareholder value through focus on revenue growth, return on capital and retention of our customers and employees. Introduce new technology to satisfy the current and future needs of our customers. A. Code of Ethics • All employees shall follow all applicable local, state, and federal codes, standards and licensing and permitting laws and ordinances regarding regulations for service and installations and any requirements for such. This includes, but is not limited to all local and state permitting, local and state licensing and local and state adopted codes and standards where required • Employees will not accept gifts from clients • Employees must sign a commitment to confidentiality contract ...
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...Company A PERT/CPM Analysis | | | | | Task Detail Table 1.1 | | | | | | | | | | | | Task | Preceding Activity | Optimistic Time to Complete (weeks) | Probable Time to Complete (weeks) | Pessimistic Time to Complete (weeks) | Expected Time to Complete (weeks) | Variance (weeks) | START | | | | | | | A | START | 2 | 3 | 4 | 3 | 0.11 | B | START | 5 | 6 | 13 | 7 | 1.78 | C | A | 3 | 4 | 8 | 4.5 | 0.69 | D | B | 10 | 11 | 15 | 11.5 | 0.69 | E | C | 4 | 5 | 6 | 5 | 0.11 | F | B | 8 | 10 | 12 | 10 | 0.44 | G | F | 4 | 6 | 11 | 6.5 | 1.36 | H | D,E | 8 | 10 | 18 | 11 | 2.78 | I | G | 3 | 6 | 12 | 6.5 | 2.25 | J | H,I | 2 | 3 | 7 | 3.5 | 0.69 | END | | | | | | | Using the formulas below I inputted the values from the chart above and found my expected time and variance. Optimistic time + 4(probable time) + pessimistic time pessimistic time - optimistic time ...
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...Company A: Demand (D) = 70,000 units per year Q* = = (2*70000)*34 = 238000 = 487.85 Ordering Costs (Co) = $34 per order 20 Per Unit Cost of inventory =400 Holding cost rate = 5% Holding cost(Ch) = $400(.05) = $20.00 Q* = 488 In order to determine the order size for Company A in the given scenario that would minimize total annual cost, I used the economic order formula. In the scenario, demand, ordering cost, unit cost and holding cost rate was given. With the numbers given I was able to determine the holding cost (per unit cost of inventory) * (holding cost rate) = holding cost. 400*.05=$20. Once this was determined, I input the numbers into the formula. I calcualted the the formula then took the square root. The answer for the order size is 488. TASK B: Company B: Demand (D) = 910,000 units per year Q* = = (2*910000)*400 = 728,000,000 64458333.33 8028.59 12*(1-(910000/15470000)) 11.29411765 Production (P) = 15,470,000 units per year ...
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...Data Expected Value Category name Value Frequency Probability Cumulative Probability Random No interval Category 1 $ 22.00 0.02 0.02 0.02 2 Category 2 $ 23.00 0.35 0.35 0.37 37 Category 3 $ 24.00 0.16 0.16 0.53 53 Category 4 $ 25.00 0.44 0.44 0.97 97 Category 5 $ 28.00 0.03 0.03 1 100 Category 6 0 1 100 Total 1 The probability for each cost is shown. The total of probability is 1. We find the cumulative probability to assign range to each category. Each category is represented by a range of random numbers between 1 to 100. To match the probability with random numbers we multiply cumulative probability by 100 So Labor Cost per Unit Random numbers 1 to 2 represents $ 22.00 Random numbers 3 to 37 represents $ 23.00 Random numbers 38 to 53 represents $ 24.00 Random numbers 54 to 97 represents $ 25.00 Random numbers 98 to 100 represents $ 28.00 so if random number is 75 then it is in range 54--97 so labor cost is $ 25 Similarly for Utilities cost Expected Value Category name Value Frequency Probability Cumulative Probability Random No interval Category 1 $ 3.00 0.36 0.36 0.36 36 ...
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...If a business wants to determine the optimale replenishment lot size, the use of the Economic Production Lot Model can be used. This model is a variation of the EOQ Model. This model procides the most optimied approach of ordering as it considers, demand, available production, ordering cost, set up costs, and holding costs in order to develop the inventory to be ordered to maintain a minimum annual cost (Rendoer 2012). Company B Details Holding Rate: 6% HR: Holding Rate Demand Units Per Year: 15,470,000 D: Demand Expected Production: 910,000 EP: Expected Production Production Cost Per Unit: $400.00 UPC: Unit Production Cost Inventory Cost Per Unit: $200.00 ICPU: Inventory Cost Per Unit *Holding Cost: $12.00 HC: Holding Cost * The holding cost is the per unit cost of inventory multiplied by the holding cost rate $200(.06) = $12.00 Process Description: The optimal lot size per order is equal to the square root of the equation of the annual demand (D). It is multiplied by 2, then multiplied by the production set up cost (UPC). Which is then divided by the holding cost (HC). Then demand (D) divided by epected production (EP), then subtracted by 1. The end result of the equation provides the optimal lot size order. The Equation: You must follow the mathmatical order of operations; simplify and solve - numerator divided by the demoniator...
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...SUBDOMAIN 309.3 - QUANTITATIVE ANALYSIS Competency 309.3.3: Expected Value Decision Analysis - The graduate uses expected value concepts as decision-making tools. Objective 309.3.3-04: Determine for a given decision tree which decision branch has the most favorable total expected value. ________________________________________ Introduction: A company is considering two alternatives for improving profits: develop new products or consolidate existing products. If the company decides to develop new products, it can either develop several products rapidly or take time to develop a few products more thoroughly. If the company chooses to consolidate existing products, it can either strengthen the products to improve profits or simply reap whatever gains are attainable without investing more time and money in the products. Given: The “Decision Tree Chart” attachment shows the predicted gains from each decision alternative described above. Gains depend on how the market reacts to the action taken by the company. The probability of each market reaction is shown on the decision tree. Task: Develop a response to the attached decision tree chart in which you: A. Calculate the expected value for each of the four decision branches. ANSWER: To determine the Expected Value (EV) you multiple the demand probability by the payoff, then add the different states of nature for the decision alternative. EV= Demand Probability (Payoff) + Demand Probability (Payoff) + Demand Probability...
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...provided in the attached worksheet: cost per unit for materials, labor, and utilities and their probability distributions. In your calculations, round to the nearest cent. Requirements: Note: When the files opens, enter your name and student ID as they appear in Taskstream into the respective boxes so the task questions and problems will populate the worksheet. If the attached template does not open or is missing information, please contact Ecare for assistance with opening the file. Note: Complete 12 trials using the random numbers that are provided on the “Simulation Template” for each probability distribution. Use the random numbers in the exact sequence that they appear on the template for each cost. A. Complete the attached “QAT1 Task 1 Spreadsheet” (responses should include two decimal...
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...QAT1 Task 5 #258453 In the given scenario, a company is considering alternatives for improving profits by either developing new products, or consolidating existing products. There are 4 separate branches that split from the 2 main branches. Develop new product: 1). Develop thoroughly: a) Good demand .47 $500,000 b) Moderate demand .38 $25,000 c) Poor demand .15 $1000 So, with the above given variables, to calculate the expected value, you multiply each probability times the corresponding payoff. Then add the results for each decision outcome. Calculations: a) .47 (500,000) = $235,000 b) .38 (25000) = $9500 c) .15 (1000) = $150 Branch 1 expected value = $244,650. 2). Develop rapidly: a) Good demand .06 $500,000 b) Moderate demand .16 $25000 c) Poor demand .78 $1000 Calculations: a) .06 (500,000) = $30000 b) .16 (25,000) = $4000 c) .78 (1,000) = $780 Branch 2 expected value = $34780 Consolidate existing product: 3). Strengthen products: a) Good demand .69 $2,000 b) Moderate demand .27 $10,000 c) Poor demand .04 $3,000 Calculations: a) .69 (2,000) = $1380 b) .27 (10,000) = $2700 c) .04 (3,000) = $120 Branch 3 expected value = $4200 4). Reap without investing: a) Good demand .32 $10,000 b) Poor demand ...
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