Concept explainers
a)
To determine: The cheapest way of producing today’s batch of the drug.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
b)
To use: The solver table to see the way the percentage of requirement B is really costing Company NA.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
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Chapter 4 Solutions
Practical Management Science
- Suppose that GLC earns a 2000 profit each time a person buys a car. We want to determine how the expected profit earned from a customer depends on the quality of GLCs cars. We assume a typical customer will purchase 10 cars during her lifetime. She will purchase a car now (year 1) and then purchase a car every five yearsduring year 6, year 11, and so on. For simplicity, we assume that Hundo is GLCs only competitor. We also assume that if the consumer is satisfied with the car she purchases, she will buy her next car from the same company, but if she is not satisfied, she will buy her next car from the other company. Hundo produces cars that satisfy 80% of its customers. Currently, GLC produces cars that also satisfy 80% of its customers. Consider a customer whose first car is a GLC car. If profits are discounted at 10% annually, use simulation to estimate the value of this customer to GLC. Also estimate the value of a customer to GLC if it can raise its customer satisfaction rating to 85%, to 90%, or to 95%. You can interpret the satisfaction value as the probability that a customer will not switch companies.arrow_forwardGiapetto 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…arrow_forwardFRUIT COMPUTER COMPANY Fruit Computer Company manufactures memory chips in batches of ten chips. From past experience, Fruit knows that 80% of all batches contain 10% (1 out of 10) defective chips, and 20% of all batches contain 50% (5 out of 10) defective chips. If a good (that is, 10% defective) batch of chips is sent to the next stage of production, processing costs of $4000 are incurred, and if a bad batch (50% defective) is sent on to the next stage of production, processing costs of $16000 are incurred. Fruit also has the alternative of reworking a batch at a cost of $4000. A reworked batch is sure to be a good batch. Alternatively, for a cost of $400, Fruit can test one chip from each batch in an attempt to determine whether the batch is defective. QUESTIONS 1.Determine a strategy so Fruit can minimize the expected total cost per batch. 2.Compute the EVSI and EVPI.arrow_forward
- A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study, and 100 subjects replied. They are informed that one group of 50 will receive a new cream and the remaining group of 50 will receive a cream with no active ingredient. The subjects are numbered 1–100 and these numbers are put into a random number generator. The first 50 unique numbers will represent the subjects that will receive the new cream and the remaining 50 subjects will receive the inactive cream. All subjects are exposed to poison ivy and given their cream. They are asked to return in three days and report their level of irritation. The average scores for each cream are compared. Does this procedure describe a completely randomized design for this experiment? O Yes, the subjects will be exposed to the poison ivy. O Yes, the subjects are randomly assigned to each treatment. O No, the subjects are…arrow_forward1. 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 filearrow_forward) 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.arrow_forward
- Prove 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.arrow_forwardA company manufactures two types of products. Each product type needs a turning process at the lathe and a milling process at the milling machine. If the lathe is used for type 1 products only, it can process 500 units in a day. If the lathe is used for type 2 products only, it can process 300 units in a day. If the milling machine is used for type 1 products only, it can proces 900 units in a day. If the milling machine is used for type 2 products only, it can process 450 units in a day. The unit profits for product types 1 and 2 are $50 and $75, respectively. Formulate an LP that will maximize the company's daily profit. (a) Decision variables? (b) Objective and objective function? (c) Constraints?arrow_forwardA certain dosage of radiation, measured in kilorads, must be given to the tumor near the brain. The dose delivered must be sufficient to kill the malignant cells but the aggregate dose must not exceed established tolerance levels for the brain. Two beams which would deliver radiation exposure to the cells will be used. The goal is to select certain beam durations that would generate the best dosage distribution by minimizing the radiation absorbed by the brain. The data for the radiation therapy is given below: a. Define the variable used: b. LP Model: c. Identify the feasible region d. Corner Points and the objective functions: e. Optimal Solution (final answer):arrow_forward
- N:B: Each question should contain Oscola Citation/reference and words limit 1000 for each question. N:B: Each question should contain Oscola Citation/reference and words limit 1000 for each question.arrow_forwardCompany XYZ is specialized in producing and selling smart watches. The company currently has two products and is planning to improve it profits in the coming years. The company is thinking of introducing a sales commission to encourage its sales people to make more sales and improve company's profitability. When designing the sales commission the company should base the sales commission on: O a. None of the given answers O b. The selling price O c. The color of the product d. The contribution margin O e. The number of employees 14:02 W A a d0) ENG 15-04-2021 re to search hp prt sc end pg up delete home 40 96 & num 2$ backspace lock 3 6. 8. V. 8 A E R U home to 4 į 5 0 enter D G J K L. pause 1 shift 2 C end alt ctrl insarrow_forwardA company has one machine which can be used to make product Alpha and product Beta. Each unit of product Alpha requires 45 minutes of machine time, while each unit of product Beta requires 37 minutes of machine time. The machine can be used for 8 hours per day and 5 days per week. Next week the company will produce 23 units of product Alpha. After completing the production of Alpha, the company will produce product Beta. How many units of product Beta can be produced next week? Use at least 4 decimals.You must showm your calculation steps and brief explanation on your Excel spreadsheets.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,