Apple wants to determine how many iPhone 14 (1) and iPhone 14 Plus (P) models to produce to maximize revenue. The price of an iPhone 14 is $800 and a iPhone 14 Plus is $900. It takes 24 production hours to make an iPhone 14 and 36 production hours to make an iPhone 14 Plus. They have 2200 production hours to make the iPhone models. Use this information to set up the linear programming problem. What is the objective function?
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- 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 simplex tableau is shown below. You should complete the tableau and respond to the questions posed. Basis CB cj JIN Cj Zj X1 3 1 X2 4 x3 0 0 5 1/2 0 1 S1 O 1/2 S2 O -1/2 6 -1/4 1 What is the current value of the objective function of the current simplex tableau? (round to 2 decimal places) 3Minimization Case. Min C = X1 + X2 + X3Subject toX1 – 3X2 + 4X3 = 5X1 – 2X2 <= 32X2 + X3 >=0And X1, X2, X3 >= 0
- Rajan 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…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.Gotham City has 10,000 streetlights. City investigatorshave determined that at any given time, an average of 1,000lights are burned out. A streetlight burns out after an averageof 100 days of use. The city has hired Mafia, Inc., to replaceburned-out lamps. Mafia, Inc.’s contract states that thecompany is supposed to replace a burned-out street lamp inan average of 7 days. Do you think that Mafia, Inc. is livingup to the contract?
- Which of the following statements is correct regarding the EMH form? Select one: None of the answers are correct If the market is weak-form efficient, then it is also semistrong and strong-form efficient. If the market is semistrong form efficient, then it is also strong form efficient If a market is strong-form efficient, it is also semistrong and weak form efficient If the market is strong-form efficient, it is also semistrong but not weak-form efficientA company is operating in two unrelated businesses. The first one is making common salt, which is sold in one kilogram consumer packs. The second business is making readymade garments. The owner of the businesses has decided to implement Materials Requirement Planning (MRP) in one of the two businesses, which is likely to give him greater benefit. Assuming that the current turnover and profits of both the units are comparable, compare the relative benefits and limitations of Materials Requirement Planning (MRP) for these two businesses.Create a spreadsheet to calculate your projected total costs, total revenues, and total profits for giving a seminar on cost estimating. Make the following assumptions: You will charge $600 per person for a two-day class. You estimate that 30 people will attend the class, but you want to change this input. Your fixed costs include $500 total to rent a room for both days, setup fees of $400 for registration, and $300 for designing a postcard for advertising. Youwill not include your labor costs for this estimate, but you estimate that you will spend at least 150 hours developing materials, managing the project, and giving the actual class. You would like to know what your time is worth given different scenarios. Youwill order 5,000 postcards, mail 4,000, and distribute the rest to friends and colleagues. Yourvariable costs include the following: $5perperson for registration plus 4 percent of the class fee per person to handle credit card processing; assume that everyone pays…
- The Math Club is selling pies on March 14th as a fundraiser. Let Q be the number of pies they make and sell. The total cost, C(Q) in dollars, for making Q pies is given by: C(Q) = 36 + 2Q. Sales price is 5 dollars for each pie. What is the additional cost to make 21 pies instead of 20 pies?The Math Club is selling pies on March 14th as a fundraiser. Let Q be the number of pies they make and sell. The total cost, C(Q) in dollars, for making Q pies is given by: C(Q) = 36 + 2Q. Sales price is 5 dollars for each pie. What is the total cost of making 20 pies?Modify Acron’s model so that development lasts for an extra year. Specifically, assume that development costs of $7.2 million and $2.1 million are incurred at the beginnings of years 1 and 2, and then the sales in the current model occur one year later, that is, from year 2 until year 21. Again, calculate the NPV discounted back to the beginning of year 1, and perform the same sensitivity analyses. Comment on the effects of this change in timing.