Johnny Hó Manufacturing Company in Columbus, Ohio, is putting out four new electronic components. Each of Ho's four plants has the capacity to add one more product to its current line of electronic parts. The unit-manufacturing costs for producing the different parts at the four plants are shown in the accompanying table C The optimal assignment of plants to components that minimizes the cost is: Component C53 C81 D5 D44 Plant 1 Plant 2 Plant 3 Plant 4 1 0.10 0.05 0.32 0.17 The cumulative cost of the optimal assignment of plants to components = dollars (round your response to two decimal places) -> 1 1 1 1 2 0.12 0.06 0.40 0.14 ▼ V ▼ V Plant 3 0.13 0.04 0.31 0.19 4 0.11 0.08 0.30 0.15
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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.33 White & Becker Tools (W&B) requires 2,000 elec- tric motors next month for its product line of weed trimmers. Each motor is composed of three com- ponents: a coil, a shaft, and housing. W&B has the capability to produce these components or purchase them from an outside vendor. The costs of produc- ing them and purchasing them are shown in the following table. COMPONENT Coil Shaft Housing DEPART- MENT PRODUCTION COST PER UNIT Fabrication 0.5 Molding 0.4 Inspection 0.2 $2.60 $1.80 $1.40 The components that are produced by W&B must pass through three departments: fabrication, molding, and inspection. The number of hours each component requires in each department and the total number of hours available next month in each department are shown in the following table: 0.2 0.7 0.3 PURCHASE COST PER UNIT COIL SHAFT HOUSING AVAILABILITY (HR.) (HR.) (HR.) (HR.) $3.12 $2.16 $1.68 0.6 0.3 0.4 3,000 3,000 1,800 In order to determine the number of components that will be produced and the number…A total of 5000 mechanical subassemblies are needed annually on a final assembly line. The subassemblies can be obtained in one of three ways: (1) Make them in one of three plants owned by the company; (2) buy them off the shelf from the one and only manufacturer; or (3) contract to have them made to specifications by a vendor. The estimated annual equivalent cost for each alternative is dependent upon specific circumstances of the plant, producer, or contractor. The information shown details the circumstance, a probability of occurrence, and the estimated annual cost. Construct and solve a decision tree to determine the least-cost alternative to provide the subassemblies.
- The Ace Manufacturing Company has orders for three similar products. Orders (units) Product A B с 1 2 Machine 3 A Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A B B IC c с Product 1 2 2,200 3 300 1,400 Capacity (units) 1,800 1,700 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20Fedori Corporation has a Parts Division that does work for other Divisions in the company as well as for outside customers. The company's Machinery Division has asked the Parts Division to provide it with 4,000 special parts each year. The special parts would require P23.00 per unit in variable production costs. The Machinery Division has a bid from an outside supplier for the special parts at P37.00 per unit. In order to have time and space to produce the special part, the Parts Division would have to cut back production of another part-the YR24 that it presently is producing. The YR24 sells for P40.00 per unit, and requires P28.00 per unit in variable production costs. Packaging and shipping costs of the YR24 are P3.00 per unit. Packaging and shipping costs for the new special part would be only P1.50 per unit. The Parts Division is now producing and selling 15,000 units of the YR24 each year. Production and sales of the YR24 would drop by 20% if the new special part is produced for…The Ace Manufacturing Company has orders for three similar products. Product A Min B C 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A B B Ic C Product 1 12 3 Orders (units) 1,900 500 1,100 Capacity (units) 1,300 1,600 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20 (a) Develop the linear programming formulation of this problem. (Let XA1 be the number of units of product A produced by machine 1, X;; be the number of units of product i produced by machine j, etc.)
- Valencia Products makes automobile radar detectors and assembles two models: LaserStop and SpeedBuster. The firm can sell all it produces. Both models use the same electronic components. Two of these can be obtained only from a single supplier. For the next month, the supply of these is limited to 4,000 of component A and 3,500 of component B. The number of each component required for each product and the profit per unit are in the table below. This question is interested in maximizing the profit). a) Identify the decision variables, objective function, and constraints in simple verbal statements. b) Mathematically formulate a linear optimization model. Components Required/Unit A B Profit/Unit LaserStop 18 6 $124 SpeedBuster 12 8 $136 Solve this question in Excel by using SOLVER. Please clearly explain what is the optimal solution? What is the resulting output of the objective function at the optimal solution? P.S. please solve in Excel.Company ZWZ manufactures three products in a serial system; Product XA is manufactured in Stage 1, Product XB in Stage 2, and XC in Stage 3. Product XB has a sales potential in the market; hence, some of it can be sold at the end of Stage 2, and the remaining can be moved to Stage 3. The third stage produces Product XC, and then delivers it to customers. Two units of Product XA produced in Stage 1 are required for each unit of Product XB in Stage 2. In addition, four units of Product XB produced in Stage 2 are required for each unit of Product XC in Stage 3. Stage 1 can only use regular time; however, Stage 2 has the options of using regular time and overtime in manufacturing. On the other hand, Stage 3 has only one alternative, which is subcontracting. The pertinent data are provided below: Stage 2 Stage 1 11 No overtime No subcontracting No sales 0.07 Unit regular time cost (TL) Unit overtime cost (TL) Unit subcontracting cost (TL) Unit selling price (TL) Unit processing time (hrs)…Cox Electric makes electronic components and has estimated the following for a new design of one of its products. Fixed cost = $23,750 Material cost per unit = $0.17 • Labor cost per unit = $0.12 • Revenue per unit = $0.67 Note that fixed cost is incurred regardless of the amount produced. Per-unit material and labor cost together make up the variable cost per unit. Assuming that Cox Electric sells all that it produces, profit is calculated by subtracting the fixed cost and total variable cost from total revenue. Construct an appropriate spreadsheet model to find the profit based on a given production level and use the spreadsheet model to answer these questions. (a) Construct a one-way data table with production volume as the column input and profit as the output. Breakeven occurs when profit goes from a negative to a positive value; that is, breakeven is when total revenue = the total cost, yielding a profit of zero. Vary production volume from 0 to 100,000 in increments of 10,000.…
- PRODUCT MIX: The JP Manufacturing Company produces two products. Resource requirements for production are given in the table. There are 1500 hours of assembly worker hours available per week, 600 hours of paint time, and 200 hours of the inspection time. Regular customers will demand at least 150 units of the regular line and 90 of the super. Formulate an LP model that will determine the optimal product mix on a weekly basis. Product Profit contribution Assembly time (hr) Paint time (hr) Inspection time (hr) Product A 50 1 1/2 1/5 Product B 75 1.5 3/4 1/5The Ace Manufacturing Company has orders for three similar products. Orders (units) Product Min A s.t. B с 1 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. Machine 2 3 LB A C B с 1 Product 112₂ 3 Machine 1 Capacity Machine 2 Capacity Machine 3 Capacity 2,200 Product A Orders Product C Orders 400 xij≥0 for all i, j. 1,400 Product B Orders Capacity (units) 1,500 1,500 Use the transportation model to develop the minimum cost production schedule for the products and machines. (a) Show the linear programming formulation. (Let XA1 be the number of units of product A produced by machine 1, X;; be the number of units of product i produced by machine j, etc.) 1,100 $1.00 $1.30 $1.10 1 $1.20…Part A is processed on a MILLING machine; Part B is processed on a LATHE machine. Two parts (A and B) are then assembled on an ASSEMBLY machine. Standard times, scrap rates, efficiency, and availability of each machine and the assembly are given in the table below. Determine the number of milling (M), the lathe (L) and the assembly (A) machines needed to produce 100 good parts from this production system during and 8-hour (480 minutes) shift. (Note: Round up the number of parts processed on each station and then round up the number of machines needed).