REQUIRED: a) Draw a network that depicts the company's supply network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. b) Formulate an optimization model to solve this problem. (Set-up only the objective function and the Constrains do not solve) Question The Audio Company produces boombows However, management has decided to subcontract out the production of the speakers needed for the boombows. The vendors are available to supply the speakers. Their price for each shipment of 1,000 speakers 1 2 > $22.700 In addition, each vendor would change a shipping cost Each shipment would go to one of the company's two warehouses. Each vendor has its own formula for calculating this shipping cost based on the mileage to the warehouse. These formulas and the mileage 1 Charge per shipment $300+0.40m
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- The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?
- Timely Transport provides local delivery service for a number of downtown and suburban businesses. Delivery charges are based on distance and weight involved for each delivery: 10 cents per pound and 15 cents per mile. Also, there is a $10 handling fee per parcel.a. Develop an expression that summarizes delivery charges.b. Determine the delivery charge for transporting a 40-pound parcel 26 miles.Kpogas produces chairs and tables. Using economic forecast for the next month, Kpogas’ marketing manager has judged that during that period, it will be possible to sell as many chairs or tables as the company can produce. Management must now recommend a production target for next month. That is, how many chairs and tables should be produced if Kpogas’ management wishes to maximize next month’s profit contribution? Making this decision requires a consideration of the following key factors: ● Kpogas’s unit contribution margin is GH¢ 5,000 on each chair that is sold and GH¢ 4,000 on each table that is sold. ● Each product is put through Kpogas’s machining operations in both department A and department B. For next month’s production, the two departments have 150 and 160 hours available time, respectively. Each chair produced uses 10 hours of machining in department A and 20 hours of machining in department B, whereas each table produced uses 15 hours of machining in department A and 10…Maximize Profit=123 L + 136 S 17 L+11 S≤ 3000 6 L+9 S≤2500 L20 and S20 (Availability of component A) (Availability of component B) Show Transcribed Text Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and SpeedBuster models. This solution gives the possible profit, which is $. (Type integers or decimals rounded to two decimal places as needed.)
- Formulate an LP model for the following problems.1. A furniture company makes two products: book shelves selling for ₱5,000 and cabinetsselling for ₱8,000. The direct cost per unit is ₱3,000 and ₱4,000, respectively. Thecompany has no difficulty in selling all the products it can manufacture. The assemblydepartment has 60 hours available per week and the finishing department can handleup to 48 hours of work per week. Manufacturing one book shelf requires 4 hours inassembly and 2 hours in finishing. Each cabinet requires 2 hours in assembly and 4hours in finishing. How can the management allocate the limited man-hour of the twodepartments in a way which will secure the largest possible net return?A firm produces three products , A , B and C , for sale both in the domestic market and in the export market and for sale to other firms . Last year domestic sales were , respectively ,50 , 60 and 80 . Exportssales were 25 , 40 and 20 . Sales to other firms were 10 , 20 and 30 . All figures are in units of thousands .This year domestic sales are expected to increase by 5% and exports sales by 10% . Sales to other firmsare expected to remain the same . The firm offers the products at the same price in all three markets Prices are currently $ 3 , $ 4 and $ 5 . Production costs for the three products are $ 2 , $ 3 and $ 4 . Find the projected profit of product A , product B and product C for this year , respectively treat the questions as products ,not fucus on product names A . ( 190 , 85 , 60) B . ( 199.5 , 93.5 , 60 ) C . ( 27.5 , 44 , 55 ) D . ( 52.5 , 63 , 84 )Please show how to solve b
- Company aims to determine the optimal number of products to be produced in order to maximize the total profit. a) Formulate the problem using algebraic method. b) Solve the model using the graphical method (indicate optimal solution and profit). C) again). Use graphical method to determine the shadow price for each of these resources (based on the definition of shadow price and by increasing each resource by one unit and solving the problem d) Use the Excel solver to do parts b and c. e) follow: Using Solver Table generate the optimal solution and the total profit for each resource as e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1) e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1) е3: Consider simultaneous changes for both unit profits in part e1 and e2 using given ranges. e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1) e5: Consider available resource of Raw material 2 (use…I. Consider the following lincar program: Max 3A + 28 LA+ I8 S 10 3A + 18 24 LA+ 28 16 A. B0 Use the graphical solution procedure to find the optimal solution. b. Assume that the objective function coefficiet for A changes from 3 to 5. Does the optimal solution change? Use the graphical solution procedure to find the new optimal solution. C. Assume that the objective function coefficient for A remains 3, but the objective fune tion coefficient for B changes from 2 to 4. Dies the optimal solution change? Use the graphical solution procedure to find the new optimal solution d. The sensitivity report for the lincar program in part (a provides the following objec- tive coefficient range information: Objective Coefficient Allowable Increase Allowable Decrease Variable LO00 1000 3.000 3.000 2000 Use this objective coefficient range informution to answer parts (b) and(C1. Given the LP model below. Do the following: a. Formulate the new LP model. b. Set up the initial table then identify the optimum column, pivotal row, entering variable out, going variable, Zj row entries, and Cj n-Zj row entries Maximize eamings = $0.80xX₁ + $0.40X₂ + $1.20X3 - $0.10X4 subject to X₁ + 2X₂ + X3 + 5X₁150 X₂ 4X₂ + 8X₂ = 70 6X₁ + 7X₂ + 2X3 - X₂ 120 X₁, X₂, X₁, X₁Z 0