Dr. Quack uses chemicals X and Y to produce two drugs. Drug A must be at least 70% of chemical X, and drug B must be at least 60% of chemical Y. Up to 40 oz of drug A can be sold at 300pesos per oz, and up to 30 oz of drug B can be sold at 250pesos per oz. up to 45 oz of chemical X can be purchased at 300pesos and up to 40 oz of chemical Y can be purchased at 200pesos per oz. create an LP and solve it using graphical method to maximize Dr. Quack's profit.
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Create a LP (Linear Programming) model for the problem and solve it using the Graphical Method.
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- Three methods can be used for producing heat sensors for high-temperature furnaces. Method A will have a fixed cost of $140,000 per year and a production cost of $62 per part. Method B will have a fixed cost of $210,000 per year and a production cost of $28 per part. Method C will require the purchase of equipment costing $500,000. It will have a life of five years and a 25% of first cost salvage value. The production cost will be $53 per part. At an interest rate of 10% per year, determine the breakeven annual production rate between the two lowest cost methods.North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of 53,000 units from Southernstar Exploration Company for $48 per unit. North Platt can manufacture the shaft at $18 per unit. Southernstar desires the diameter of the shaft to be 1.278 cm. The diameter of the shaft must not be less than 1.253 cm in order to fit properly inside the sleeve. To be able to insert the shaft into a sleeve without the use of force, the diameter cannot be larger than 1.303 cm. A defective shaft is discarded and a replacement has to be shipped via express freight to locations around the world. North Platt estimates that the average cost of handling and shipping a replacement shaft will be approximately $38. Shown below are the diameters from a sample of 100 shafts manufactured during a trial run: Diameter 1.235 1.243 1.253 1.261 1.265 1.273 1.275 Number of Units 2 3 4 3 3 4 7 Diameter 1.276 1.277 1.278 1.279 1.280 1.283 1.291 Number of Units 7…North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of 58,000 units from Southernstar Exploration Company for $68 per unit. North Platt can manufacture the shaft at $38 per unit. Southernstar desires the diameter of the shaft to be 1.283 cm. The diameter of the shaft must not be less than 1.258 cm in order to fit properly inside the sleeve. To be able to insert the shaft into a sleeve without the use of force, the diameter cannot be larger than 1.308 cm. A defective shaft is discarded and a replacement has to be shipped via express freight to locations around the world. North Platt estimates that the average cost of handling and shipping a replacement shaft will be approximately $58. Shown below are the diameters from a sample of 80 shafts manufactured during a trial run: Diameter 1.240 1.248 1.258 1.266 1.270 1.278 1.280 Number of Units 1 2 3 2 2 3 6 Diameter 1.281 1.282 1.283 1.284 1.285 1.288 1.296 Number of Units 6 7…
- North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of 43,000 units from Southernstar Exploration Company for $48 per unit. North Platt can manufacture the shaft at $18 per unit. Southernstar desires the diameter of the shaft to be 1.289 cm. The diameter of the shaft must not be less than 1.264 cm in order to fit properly inside the sleeve. To be able to insert the shaft into a sleeve without the use of force, the diameter cannot be larger than 1.314 cm. A defective shaft is discarded and a replacement has to be shipped via express freight to locations around the world. North Platt estimates that the average cost of handling and shipping a replacement shaft will be approximately $38. Shown below are the diameters from a sample of 80 shafts manufactured during a trial run: Diameter 1.246 1.254 1.264 1.272 1.276 1.284 1.286 Number of Units 1232236 Diameter 1.287 1.288 1.289 1.290 1.291 1.294 1.302 1. Expected loss 2.…Giapetto is thinking of buying a new cutting tool for $25 to make toy soldiers and a new clamping tool for $20 to make toy trains. If he does not buy a new tool, he can still make a toy using the older tool he already has. However, using an old cutting tool leads to 50% of the produced soldiers and using an old clamping tool leads to 40% of the produced trains to be defective. With a new tool, there is no defective production. Giapetto cannot sell any defective product. Weekly demands (must be met exactly without left-over inventory) and productions costs are as follows: 1. Soldiers 2. Trains Demand (units/week) Production cost (S/unit) 100 300 12 14 There are other details about the problem which will be added later. Giapetto started formulating a mathematical model considering only the above description and defined the following decision variables: yi: Production quantity for type i toy, i = 1, 2 corresponding to soldiers and trains, respectively. Considering the above problem…A company makes parts that cost $35.00 in material and labor. 92% of the parts are produced defect free and are sold for full price at $110 each. 2% of the parts made must be scrapped. Scrap parts are sold for $8.00 each. The remaining 6% of the parts made must be reworked at a cost of $12.00 each. After rework 1% still must be scrapped and the other 5% is sold at a discounted price of $90 each. a. Draw the tree diagram showing the quality cost situation. b. Determine the earnings per part. c. Determine the cost of poor quality (COPQ). d. Determine the earnings per part and COPQ if the rework operation was shut down and the parts that required reworking were just sold for scrap instead.
- The Collector's Choice Inc. (CCI), a luxury car import company, has an old warehouse at the Port of Miami, Florida, where it temporarily stores expensive sports cars and automotive parts that arrive from Europe. This summer, CCI has noticed that the termite infestation in the warehouse has escalated to a point where tenting cannot be postponed anymore. (Tenting is the process of wrapping a building inside a huge tent that is subsequently filled with a poisonous gas capable of killing most forms of life inside, including insects, plants, pets, and human beings.) CCI's pest control company's contract specifies a to-do list of pre-tenting tasks, which include: • Turning off all air-conditioning units and opening all windows of the warehouse • Turning off all internal and external lights, including those operating on a timer • Pruning all outdoor vegetation at least 18" away from the -warehouse • Soaking the soil around the warehouse on the first day of tenting The requirement of opening…1. A certain dosage of radiation, measured in kilorads, must be given to the tumor near the brain. The dose delivered must be sufficient to kill the malignant cells but the aggregate dose must not exceed established tolerance levels for the brain. Two beams which would deliver radiation exposure to the cells will be used. The goal is to select certain beam durations that would generate the best dosage distribution by minimizing the radiation absorbed by the brain. Determine the optimal exposure times for beam 1 and beam 2. The data for the radiation therapy is given below: Fraction of dose absorbed per second Average dosage Area Beam 1 Beam 2 (in kilorads) Brain 0.4 0.5 Spine 0.3 0.1 At most 2.7 Tumor 0.5 0.5 At most 6 Center of Tumor 0.6 0.4 At least 6 1 Add fileProve the following using strong induction. Suppose you are gifted a collection of 3n pokéballs; all of the the pokéballs have the same size and weight except for one which is slightly heavier, and otherwiselook and feel exactly the same as the others. You are tasked with identifying theheavy pokéball and have at your disposal a set of balancing scales which can be usedto compare the weights of two collections of pokéballs. The scales can show whetherthe two collections have the same weight, or can show which collection is heavier if theweights are different. Prove using strong induction that you can identify the heavypokéball out of 3n pokéballs using n weighing operations.
- ) Creative Sports Design (CSD) manufactures a standard-size racket and an oversize racket.The firm’s rackets are extremely light due to the use of a magnesium-graphite alloy that wasinvented by the firm’s founder. Each standard-size racket uses 0.125 kilograms of the alloy andeach oversize racket uses 0.4 kilograms; over the next two-week production period only 80kilograms of the alloy are available. Each standard-size racket uses 10 minutes of manufacturingtime and each oversize racket uses 12 minutes. The profit contributions are $10 for eachstandard-size racket and $15 for each oversize racket, and 40 hours of manufacturing time areavailable each week. Management specified that at least 20% of the total production must be thestandard-size racket. How many rackets of each type should CSD manufacture over the next twoweeks to maximize the total profit contribution? Assume that because of the unique nature oftheir products, CSD can sell as many rackets as they can produce.Clippers Inc. (CI) manufactures two types of garden clippers. A light-duty model, called the “half-inch,”is intended for clipping branches and stems up to one-half inch thick. The “one-inch” model is designedfor heavier stems and branches. To boost sales, CI decided at the beginning of the current year to reducethe price of the half-inch model to better position its price relative to some key competitors. On the otherhand, CI felt that the one-inch model was technically superior to competitors’ models and decided that asmall price increase was appropriate. The data for the current and prior year are as follows:Current Year Prior YearSales units 7,200 6,500Sales mix for each productHalf-inch model 50% 30%One-inch model 50% 70%PriceHalf-inch model $12.00 $14.00One-inch model $36.00 $32.00Variable cost per unitHalf-inch model $6.00 $6.00One-inch model $8.00 $8.00Fixed cost $35,000 $35,000Required1. Prepare a comparative contribution income statement for CI for the current year that shows…A mixture of pellets is to be made containing x regular pellets, y large pellets and z extra large pellets. Cost, weight and volume data for each type of pellet are shown in the table. Is it possible to make mixture of 55 pellets at a cost of $0.85 if the mixture is to have 120 weight units and 130 volume units? If so, how many each type of pellet should be in the mixture? Pellet Type 5. Number of Cost per Pellet in Cents Weight Units per Pellet Volume Pellets Units per Pellet Regular Large Extra large 2 1 4 y 1 4 3