LINEAR PROGRAMMING. A garment manufacturing has already finished garments to iron/press in order to prepare for selling them in the market. There are two kinds of garments, namely: poloshirt and t-shirts. Poloshirt is to be sold at P200 per piece while t-shirt at P50 each. Ironing/pressing one piece of polotshirt takes 30 minutes while t-shirt takes 12 minutes. The owner of the garment factory has a total of 7 finishing workers, who each works 8 hours per day. Four (4) of which are assigned as pressers and three (3) as packagers. For one day, the owner would like to maximize his profit.
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- A furniture factory makes two types of wooden tables,large and small. See the flowchart below.SetupTime,MinutesRun Timeper Piece,MinutesCapacity,Piecesper HourWood cutting 30 5 15Make four legs 60 10 10Make tops 60 12 8Finish the wood 20 8 12Assemble and ship 20 17 14 Small tables are made in batches of 100, and large tables are made in batches of 50. A batch includes a fixed setup time for the entire batch at each process step and a run time for each piece in the batch. Both large and small tables have the same processing times. The capacities of each process step are given, and apply to production of either type of table, as shown in the flowchart.a. What is the capacity of the system, and what is the bottleneck?b. What are the throughput times for batches of large and small tables?c. When producing at a rate of six small tables per hour on average, how many tables will be in the system?Tuff-Rider, Inc., manufactures touring bikes and mountainbikes in a variety of frame sizes, colors, and component com-binations. Identical bicycles are produced in lots of 100. Theprojected demand, lot size, and time standards are shown inthe following table: Item Touring MountainDemand forecast 5,000 units/year 10,000 units/yearLot size 100 units 100 unitsStandard processing time .25 hour/unit .50 hour/unitStandard setup time 2 hours/lot 3 hours/lot The shop currently works 8 hours a day, 5 days a week,50 weeks a year. It operates five workstations, each producingone bicycle in the time shown in the table. The shop main-tains a 15 percent capacity cushion. How many workstationswill be required next year to meet expected demand withoutusing overtime and without decreasing the firm’s currentcapacity cushion?Purple Swift manufactures birdhouses in lots of 10. Eachbirdhouse takes 45 minutes to paint. After 10 birdhouses arepainted, the company switches paint color which requires aone hour changeover. The company works 8 hours per shift,one shift per day, 220 days per year. Currently the companyhas one paint booth. What is Purple Swift’s paint capacitycushion if it builds 2,000 birdhouses per year?
- Three departments- milling (M), drilling (D), andsawing (S)- are assigned to three work areas in Victor Berardis'smachine shop in Kent, Ohio. The number of workpieces movedper day and the distances between the centers of the work areas,in feet, follow. Pieces Moved between Work Areas Each Day lt costs $2 to move I workpiece I foot.What is the cost?3.4-15. The Weigelt Corporation has three branch plants with ex- cess production capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants have this capability, so some of the excess capacity can be used in this way. This product can be made in three sizes-large, medium, andAccompany makes two products (1&2) each product requires time on two machines (A&B). specification for each product is as follows. Product1 product2 Processing time on Machine A (hrs/unit) 2 2 Processing time on Machine B (hrs/unit) 1 2 Material and labour cost ( ksh/unit) 14 15 Selling price (ksh/unit) 16 18 Maximum possible sale (units) 130 150 The amount of time available on machine A is 360 hours and on machine B is 260 hours. Formulate the linear programme which, when…
- A processor makes two components, A and B, which are then packaged together as thei nal product (each product sold contains one A and one B). The processor can do onlyone component at a time: Either it can make As or it can make Bs. There is a setup timewhen switching from A to B.Current plans are to make 100 units of component A, then 100 units of component B,then 100 units of component A, then 100 units of component B, and so forth, where thesetup and run times for each component are given below.Component Setup/Changeover Time Run Time/UnitA 5 minutes 0.2 minuteB 10 minutes 0.1 minuteAssume the packaging of the two components is totally automated and takes onlytwo seconds per unit of the i nal product. This packaging time is small enough that youcan ignore it. What is the average hourly output, in terms of the number of units of packagedproduct (which includes one component A and one component B)?A production process at Kenneth Day Manufacturing is shown in the figure below. The drilling operation occurs separately from, and simultaneously with, the sawing and sanding, which are independent sequential operations. A product needs to go through only one of the three assembly operations (the operations are in parallel). Q 2.1 units/hr Sawing 5 units/hr Sanding Drilling 5 units/hr Welding 2.5 units/hr a) Sawing is the bottleneck. b) The bottleneck time is 28.57 minutes per unit (round your response to two decimal places). c) The throughput time of the overall system is minutes (round your response to two decimal places). Assembly 0.8 units/hr Assembly 0.8 units/hr Assembly 0.8 units/hrUp, Up, and Away is a producer of kites and wind socks.Relevant data on a bottleneck operation in the shop for theupcoming fiscal year are given in the following table:Item Kites Wind SocksDemand forecast 30,000 units/year 12,000 units/yearLot size 20 units 70 unitsStandard processing time 0.3 hour/unit 1.0 hour/unitStandard setup time 3.0 hours/lot 4.0 hours/lotThe shop works two shifts per day, 8 hours per shift, 200 daysper year. Currently, the company operates four machines,and desires a 25 percent capacity cushion. How many ma-chines should be purchased to meet the upcoming year’s de-mand without resorting to any short-term capacity solutions?
- Tuff-Rider, Inc., manufactures touring bikes and mountain bikes in a variety of frame sizes, colors, and component combinations. Identical bicycles are produced in lots of 90. The projected demand, lot size, and time standards are shown in the following table: LOADING... Item Touring Mountain Demand forecast 4,000 units/year 12,000 units/year Lot size 110 units 90 units Standard processing time 0.30 hour/unit 0.75 hour/unit Standard setup time 2 hours/lot 3 hours/lot The shop currently works 8 hours a day, 5 days a week, 50 weeks a year. It operates five workstations, each producing one bicycle in the time shown in the table. The shop maintains a 15 percent capacity cushion. How many workstations will be required next year to meet expected demand without using overtime and without decreasing…Each A (finished product) requires 1 of component B and 2 of component C. Each B requires 2 of part D and 1 of part E and each C requires 1 of part D and 1 of part F.If the demand for product A is 50 units., and there are 15 units of B on hand and 50 units of C, how many units of Part D will be needed?O 1000 workers are currently working in Sigma Manufacturing Industry. This industry is paying the wages to its workers on a daily basis. No vacation is given for any occasion in this industry. The factory is running from 8:30 am to 5:30 pm with a lunch break of 60 minutes. This break is not counted as working hours. Last year, 10 accidents occurred which caused almost 50 injuries. Around 50 people remain absent everyday in this industry. Gama Production Factory was a sister concern of Sigma Manufacturing Industry which is closed now. It had half of the workers of Sigma. In 2017, 50 accidents occurred and each accident caused 3 injuries and a loss of 8 hours each on an average. Working hours and attendance rate were the same as Sigma Manufacturing Industry. Now compute the frequency rate and severity rate for Gama Production Factory. Also, illustrate the kinds of key accident data you should collect from the place where an accident has occurred.