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_forwardRajan wanted a radio from Jacky's. It appears that Rajan is particularly interested in purchasing a Radio from the inexpensive retailer's sales manager for consumer electronics. He tells Jacky, the salesperson at the inexpensive store where he thinks he'll get the best deal, that his old radio died and he wants to listen to his favourite tunes. He wants a replacement radio as quickly as possible. In three and a half weeks, Rajan's favourite model will be 10% off.He suspects Rajan won't wait and will find another job. Jacky will earn less on the lowered price. He thinks that telling Rajan of the sale makes little sense.When Jacky tells Rajan that the radio set he wants is no longer available and won't be for another week, Rajan is enraged. Fearing losing the business, Jacky begs his sales manager, Michelle, to speed up delivery. Michelle says it's impossible and suggests Jacky tell Rajan the store can get the set in 24 hours and sell him the demo model. Michelle says the sample is new…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_forward
- FRUIT 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_forwardMemanarrow_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
- A 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_forwardThe general expressions for the two direct stress components of a plane stress field have the form: 011 022 = ax + bxx2 + cx₁x² + dx kx3 + lxx₂+mx₁x² + nx = where a, b, c, d, k, l, m, n are constants. Determine the necessary relationship for these constants if the stress distribution is to be compatible. For the special case where a = c = d = k = m =0, determine expressions for the compatible stress components σ11, 022, and 012arrow_forwardProve 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_forward
- A 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_forwardA political party is planning a half-hour television show. The show will have at least 3 minutos of direct requests for money from viowers Three of the party's politicians will be on the show-a senator, a congresswoman, and a governor The senator, a party "elder statesman," demands that he be on screen for at least twice as long as the governor The total time taken by the senator and the governor must be at least twice the time taken y the congresswoman Based on a pre-show survey, it is believed that 33, 38, and 43 (in thousands) viewers will watch the program for each minute the senator, congresswoman, and governor, respectively, are on the air. Find the time that should be allotted to each politician in order to get the maximum number of viewers Find the maximum number of viewers The quantity to be maximized, z, is the number of viewers in thousands. Let x, be the total number of minutes allotted to the senator, x, be the total number of minutes allottod to the congresswoman, and x,…arrow_forwardA cement mix company is renowned for providing high strength concrete additives - at high unit cost. It delivers two types of cement additives - Tuf and Rok. In making these additives the company adds two special products, Qikcem and Plascem. These additives contain two (2) basic ingredients: Lime and Flyash, in different proportions, as shown in the table below. Flyash [%] Lime Cost Special Products Qikcem (1) Plascem (2) Availability [kg/hr] 2600 3600 [%] [S/kg] 10 15 45 55 35 65 The cement additive, Tuf should not contain more than 70% of Lime and the cement additive, Rok must contain at least 45% of Flyash. The company can sell at most 800oerkg of its additive products (Tuf and Rok) per hour. There are other limitations and local requirements, as stated beklew: a) Due to the plant installed capacity and personnel requirements, no more than 6000 kg/hour of Tuf can be produced b) The plant has contracted to deliver at least 3500 kg/hour of Tuf c) The company is restricted, by local…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,