Wk Qu. 8-13 A firm offers three different prices on its...A firm offers three different prices on its products, depending upon the quantity purchased. Since availableresources are limited, the firm would like to prepare an optimal production plan to maximize profits. Product 1 hasthe following profitability: $11 each for the first 70 units, $10 each for units 71–170, and $9 for each unit over 170.Product 2's profitability is $11 each for the first 45 units, $10 each for units 46–120, and $9 each for each unit over120. The products each require 3 raw materials to produce (see table below for usages and available quantities).Available Quantity(pounds)Product 1 usage (pounds Product 2 usage (poundsRaw Materialper unit)per unit)А41,600В12101,000C1072,000Use separable programming to find the optimal production plan.(Leave no cells blank – be certain to enter "0" wherever required. Round the first two answers (units of Product1 and 2) to the nearest whole number. Round the total profit answer to 2 decimal places and use unrounded unitquantities to compute it.)units of Product 1 andunits of Product 2.The total profit from this plan will be

A production plan exhibits stimulating support or guides a plan and production of a particular item…

Answered: Wk Qu. 8-13 A firm offers three…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 59P

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2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed…
2) A buyer for a large sporting goods store chain must place orders for professional footballs with the footballmanufacturer six months prior to the time the footballs will be sold in the stores. The buyer must decidein November how many footballs to order for sale during the upcoming late summer and fall months.Assume that each football costs the chain $45. Furthermore, assume that each can be sold for a retail priceof $90. If the footballs are still on the shelves after next Christmas, they can be discounted and sold for$35 each. The probability distribution of consumer demand for these footballs (in hundreds) during theupcoming season has been assessed by the market research specialists and is presented below. Finally,assume that the sporting goods store chain must purchase the footballs in lots of 100 units. Demand Probability 4 0.30 5 0.50 6 0.20 a) Construct a decision tree…
1. Suppose you are going on a weekend trip to a city that is d miles away. Develop a model that determines your round-trip gasoline costs. What assumptions or approximations are necessary to treat this model as a deterministic model? Are these assumptions or approximations acceptable to you? 2. Suppose that a manager has a choice between the following two mathematical models of a given situation: (a)a relatively simple model that is a reasonable approximation of the real situation, and (b)a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?
E The Apex Television Company has to decide on the number of 27- and 20-inch sets to be produced at one of its factories. Market research indicates that at most 40 of the 27-inch sets and 10 of the 20-inch sets can be sold per month. The maximum number of workhours available is 500 per month. A 27-inch set requires 20 work-hours and a 20-inch set requires 10 work-hours. Each 27-inch set sold produces a profit of $120 and each 20-inch set produces a profit of $80. A wholesaler has agreed to purchase all the television sets produced if the numbers do not exceed the maxima indicated by the market research. Formulate a linear programming model for this problem and use graphical method to solve it
1. A distillery produces two types of alcohol for filling and distributing, the regular beer and the premium beer. A batch of regular costs $375 to manufacture and a container of the Premium beer costs $420. The manufacturer wishes to establish the weekly production plan that minimizes cost. Production of these products is limited to processing, testing and material. Each batch of regular beer requires 4 hours processing whereas each batch of premium requires 2 hours of processing. Further each batch of regular requires 4 hours of testing compared to 6 hours of testing for a batch of Super. A batch of regular and a batch of Super each require 1 litre of material. Processing and testing have a maximum of 100 and 180 hours available and the total material available is 40 litres. Because of an agreement, the sales of regular beer are limited to a weekly maximum of 20 batches and to honour an agreement with a loyal distributor, at least 10 batches of premium beer must be sold each week.…
Show the complete Linear Programming Model. Show solutions (i.e. decision variables, objective function, subject to constraints, etc.) Q. A gold processor has two sources of gold ore, source A and source B. In order to keep his plant running, at least three tons of ore must be processed each day. Ore from source A costs $1,000 per ton to process, and ore from source B costs $500 per ton to process. Costs must be kept to less than $4,000 per day. Moreover, Government Regulations require that the amount of ore from source B cannot exceed twice the amount of ore from source A. If ore from source A yields 2 oz. of gold per ton, and ore from source B yields 3 oz. of gold per ton, how many tons of ore from both sources must be processed each day to maximize the amount of gold extracted subject to the above constraints? Formulate the LP model.
2. A canning company produces two sizes of cans—regular and large. The cans are produced in 10,000-can lots. The cans are processed through a stamping operation and a coating operation. The company has 30 days available for both stamping and coating. A lot of regular-size cans require 2 days to stamp and 4 days to coat, whereas a lot of large cans requires 4 days to stamp and 2 days to coat. A lot of regular-size cans earn $800 profit, and a lot of large-size cans earn $900 profit. In order to fulfill its obligations under a shipping contract, the company must produce at least nine lots. The company wants to determine the number of lots to produce of each size can (and) in order to maximize profit. 8. In Problem 2, how much flour and sugar will be left unused if the optimal numbers of cakes and Danish are baked?
Q. A gas company owns two refineries, 32 LPG bottling plants, and 367 retail outlets. The company has eight executive grades. The first four grades are classified as a junior. Management, fifth and sixth as middle and seven and eighth as top management. Due to unsystematic career management, the company has landed in the peculiar problem of 70% executive strength getting cumulated in the middle grades. For instance, there are 512 executives in the middle management category against the actual requirement of 84. Further, 245 out of these 512 are due to be promoted to the top management category but vacancies are only 27. Due to this lack of adequate career up gradation opportunities. Many in the middle level are frustrated and lack the motivation to perform.1. How do you develop a career planning and development in performance management?2. Discuss what strategy this company must adopt to overcome this situation?
13 In addition to the legislation and guidelines that may apply, the investment policythat is decided upon by the investment manager (for a client) should include allthe following elements EXCEPT rate of return expectations (including timeframe) and expected volatility specific goals about continuing education an investment review process the asset classes for investment a policy review process
5. Daniel is planning to earn money over the summer mowing lawns in the neighborhood to buy a scooter. The scooter he wants costs $2,200. He will be charging $19.1/lawn and estimates his costs to be $2.7/lawn. How many lawns must he mow in order to pay for the scooter entirely through his earnings? a. 115.18 b. None of the other options. c. -134.15 d. 134.15 e. 112.48 f. 2562.20
1.A clockmaker makes two types of woodenclocksto sell at various malls. It takes him three hours to assemble a pine clock, which requires two oz of varnish. It takes four hours to assemblea molave clock, which takes four oz of varnish. He has eight oz of varnish available in stock and can work 12 hours. If he makes a P100 profit on each pine clock and P120 on each molave clock, how many of each type should he make to maximize his profit?2.A biologist is developing two new strains of bacteria. Each sample of Type A bacteria produces five new viable bacteria,and each Type B bacteria produces six new viable bacteria. Altogether, at least 150 new viable bacteria must be produced. At least 10, but not more than 20,of the original sample,must be Type A,and not more than 60 of the samples must be Type B. A sample of Type A costs P500,and a sample of Type B costs P700. If both types are to be used, how many samples of each type should be used to minimize the cost?
1. The marketing concept states that a firm must put consumer needs first, even if it means foregoing satisfactory profits. a. True b. False 2. John wants to start his own fruit juice and beverage company. He is aware of the large number of competitors in this industry and of the fact that his product should not be very costly. To differentiate his product from that of his competitors, he decides to sell his beverages in specially designed containers that keep the juice fresh for 7 days even without refrigeration. John is focusing on the _____component of the marketing mix. a. Place b. Pricing c. Packaging d. Product 3. The sales of a product are rising rapidly and profits are peaking. This product is in the _____ stage of the product life cycle. a. Introduction b. Growth c. Maturity d. Decline 4. A(n) _____ is given to customers for accepting less of something or as an adjustment for variation in quality. a. Discount b.…

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