Subject: Valu-Com Electronics manufacturing difference telecom type card (TEC) for computers and Laptop As summarized in the table as below, each type of equipment asked difference amount about PC Board, Resistors, memory Chips, and Assembly Labor Per Unit Requirements Hyperlin Fastlink Speedlink Microlink k PC Board (inch Etherlin k 20 15 10 Resistors 28 24 18 12 16 Memory Chips 8 4 0.75 0.6 0.5 0.65 square) Assembly Labor (hour) Mức giá bán sỉ đơn vị giá thành cho kiểu TEC sau: Per unit revenues and costs ($) Hyperlin Fastlink Speedlink Microlink k Etherlin k Whole sale price 189 149 129 169 139 Cost 136 101 96 137 101 In next the period of production, Valu-com are available 80,000.00square inch PC board, 100,000.00 Resistors, 30,000.00 Memory chips and 5,000.00 Assembly labor The company can sell all off the product, however the marketing Dept wants to make sure that the company must produce at least 500 product each type and the number of Fastlink by twice as Hyperlink card and the company want to maximize profit a Let's build LP's model for this problem b Creat a speadsheet model for this problem and solve it by Solver in excel c What is the optimal plan? d Is Valu-Com can earn more money if it arranged for assembly workers to work overtime? Now let's Solver to create a senssitivity analysis report for the problem and answer the next question e Resources (Control conditions) in the above problem is to be used up? f If the company want to remove the product, it should remove empty? g If the company can buy another 1000 Memory Chips with the same cost, whether it, and how much additional profit is it? Task Question 1: Building an optimal model (LP) to the problem? In order to build the optimal model (Linear Programming) to Calu-com Electronics, based on the goods which the company produces are telecom cards, we shall assume that each type of card and the cost of telecomunications is a variable, detail as follows: Name of goods Good's variable Cost's variable Hyperlink X1 C1 Fastlink X2 C2 Speedlink X3 C3 Microlink X4 C4 Etherlink X5 C5 We have equated the linear programming (LP) to the problem as follows: Max: C1X1 + C2X2 + C3X3 + C4X4 + C5X5 In which: Profit = Unit price- equivalent cost Ci = Pi - Ti At the request of the company marketing department, the company must produce at least 500 units per type and the Fastlink card number more than times Hyperlink card number To maximize profit, the following equation are: X1 + X2 + X3 + X4 + X5 > 500 X2 > 2X1 -> X2 - 2X1 > On the basis of available materials include 80,000 square inch of the PC Board; 100,000 Resistors; 30000 Memory Chips, and 5000 hours of labor: 20X1 + 15X2 + 10X3 + 8X4 +5X5 < 80.000 28X1 + 24X2 + 18X3 + 12X4 +6X5 < 100.000 8X1 + 8X2 +4X3 +4X4 + 6X5 < 30.000 0,75X1 + 0,6X2 +0,5X3 + 0,65X4 + 1X5 < 5.000 Question 2: Creating models and solve problems by Solve? - Create a model problem: TEC PRODUCTION Hyperlink Fastlink Speedlink Microlink Etherlink Decision Variable 500 1,000 1,500 2,250 500 Price 189 149 129 169 139 Cost 136 101 96 137 101 Total profit Unit Profit 53 48 33 32 38 215,000 Constraints Used PC board 20 15 10 60500 Resistors 28 24 18 12 16 100000 Memory chips 8 4 30000 Assembly labor 0.75 0.60 0.50 0.65 1.00 3687.5 Demand 500 500 500 500 500 - Solve: Microsoft Excel 14.0 Answer Report Worksheet: [Book1]Sheet1 Report Created: 02/22/2014 16:42:17 PM Result: Solver found a solution All constraints and optimality conditions are satisfied Engine: Standard LP Simplex Solution Time: 00 Seconds Iterations: Subproblems: Incumbent Solutions: Target Cell (Max) Cell Name Original Value Final Value 10 $H$14 Labor Used 3737.5 $H$14=2*R3C3 Binding $C$3 Decision Variable 500 $C$3>=$C$16 Binding 16 $D$3 Decision Variable 1000 $D$3>=$D$16 Not Binding 500 $E$3 Decision Variable 1500 $E$3>=$E$16 Not Binding 1000 $F$3 Decision Variable 2250 $F$3>=$F$16 Not Binding 1750 17 $G$3 Decision Variable 500 $G$3>=$G$16 Binding Microsoft Excel 14.0 Sensitivity Report Worksheet: [Book1]Sheet1 Report Created: 02/22/2014 16:42:17 PM 18 Target Cell (Max) Cell Name Final Value $H$8 19 Unit Profit Total profit 215000 Adjustable Cells 20 Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$3 Decision Variable 500 -43.6666667 53 43.66666667 1E+30 $D$3 21 Decision Variable 1000 48 16 1E+30 $E$3 Decision Variable 1500 33 15 $F$3 Decision Variable 2250 32 5.272727273 22 $G$3 Decision Variable 500 -9.66666667 38 9.666666667 1E+30 Constraints 23 Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H Side Increase Decrease $H$11 PC board Used 60500 80000 1E+30 19500 24 $H$12 Resistors Used 100000 0.166666667 100000 10500 6000 $H$13 Momory chips Used 30000 7.5 30000 2000 2333.333333 $H$14 Labor Used 3737.5 5000 1E+30 1262.5 25 $D$3 Decision Variable 1000 -16 875 500 Question 3: What is the optimal plan? It depend on optimization are Max y= f(xi) or Min y=f(xi) in which: i: 1………n: is decision terms f(x1…………xn) = bn is constraint terms In this case, with the limited resources given as: PC board, Reristors, Memory chips, labor to gain recognition highest ($ 215,000) from the card manufacturer telecommunications, Valu-Com Electronics to produce the type of card numbers as follows: - Hyperlink: 500 cards - Fastlink: 1.000 cards; - Speedlink: 1.500 cards; - Microlink: 2.250 cards; - Etherlink: 500 cards 26 Question 4: Is Valu-Com can earn more money if it arranged for assembly workers to work overtime? We see in the spreadsheet model, the use of resources to produce materials telecommunications card (PC board, resistors, Memory Chips) and Labor (Labor), the labor resources have not been used all: only 3,738 hours of use compared to available resources is 5,000 hours Due to arranging the workers to assemble hardwork will not help Valu-Com Electronics earn more money Using Solver to create a sensitivity analysis report: Cell Name $H$8 Unit Profit Total profit Final Value 215,000 Reduce Cell Name(Decision Final d Objective Variable) Hyperlink: $D$3 Allowabl e e Coefficien Value $C$3 Allowabl Cost t Decreas Increase e 500 -43.67 53 43.67 1E+30 Fastlink: 1,000 0.00 48 16.00 1E+30 $E$3 Speedlink: 1,500 0.00 33 15.00 $F$3 Microlink : 2,250 0.00 32 1.00 5.27 $G$3 Etherlink : 500 -9.67 38 9.67 1E+30 Constrain Allowabl Allowabl Cell Name Final Shadow t e e Value Price R.H Side Increase Decreas 27 e $H$1 PC board Used 60,500 0.00 80,000 1E+30 19,500 Resistors Used 100,000 0.17 100,000 10,500 6,000 30,000 7.50 30,000 2,000 2,333.33 $H$1 $H$1 Memory chips Used $H$1 Labor Used 3,738 0.00 5,000 1E+30 1262.5 $D$3 Decision Variable 1,000 -16.00 875 500 Question Resources (control conditions) in this problem are used up? There are two ways to do: Looking at the sensitivity analysis report in constrain part, to compare the column value and constrain R.H.Side column These resources have been used up in the production are: Resistors, Memory Chips Question If the company want to remove the product, it should remove empty? On the basis of the formula for calculating the added value of the objective function, we have: Profit = Unit cost - material cost = Ci - ∑QiSi We have: Hyperlink unit profit = (189-136) - (20*0+28*0,17+8*7,5+0,75*0)= -11,76 28 Fastlink unit profit = (149-101) - (15*0+24*0,17+8*7,5+0,6*0)= -16,08 Speedlink unit profit = (129-96) - (10*0+18*0,17+4*7,5+0,5*0)= -0,06 Microlink unit profit = (169-137) - (8*0+12*0,17+4*7,5+0,65*0)= -0,04 Etherlink unit profit = (139-101) - (5*0+16*0,17+6*7,5+1*0)= -9,72 Conclusion: Based on the above results, due to the unit's profit Fastlink is the lowest, thus if you remove one product should give Fastlink production Question 7: If the company can buy another 1000 Memory Chips with the same cost, whether it, and how much additional profit is it? We have a new LP charts with conditions controlled of Memory chips are 31,000, we have been using the solver results as follows: I see the difference in profit is: 225,500- 215,000= $7,500 (*) This should be done because the profitability of production will increase as $ 29 7,500 30