5.A company makes two types of products, A and B. These products are produced during a 40-hrwork week and they are shipped out at the end of the week. Each product requires 20 and 5 kgof raw material, respectively, and the company has access to 9500 kg of raw material per week.Only one product can be created at a time, with production times for each of 0.04 and 0.12 hr,respectively. Finally, the company makes profits of $45 and $20 on each unit of A and B,respectively.a)b)Set up the linear programming problem to maximize profit.Solve the linear programming problem graphically.6. Solve problem (5) using the simplex tableau method.

Suppose- X1 be the no. of units for product A to be makeX2 be the no. of units for product B to be…

Answered: 5. A company makes two types of…

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. 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?
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?
2. A firm makes two products X and Y and has a total production capacity of 9 tons per day.X and Y requiring the same production capacity. The same has a permanent contract to supply at least two tons of X and at least 3 tons of Y per day to another company. Each ton of X requires 20 machine hours of production time and each ton of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. The entire firm's output can be sold and profit made is 80 R.O of X and 120 R.O per ton of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. Formulate a LPP.
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?
4. Which statements are true of optimization? Select one or more: a. It is a general mathematical tool and can be used not only in portfolio optimization but many business problems b. When applied in real world setting we often use computers to estimate the optimum numerically rather than doing calculus by hand c. One of the earliest applications of optimization to business problems is Augustin Cournot's 1838 duopoly pricing model d. Optimization can only ever be as effective as the description of the objective function e. The selection of the FOC at zero is an arbitrary choice but allows for the identification of inflection (turning points) in the objective function f. When optimizing by hand you differentiate the objective function with respect to the control variables of the economic entity at hand
2. A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal is to maximize profit, what would be the appropriate objective function? Select one: a. Maximize profit Z = $10Y + $25Z b. Maximize profit Z = 0.25Y + 0.20Z c. Maximize profit Z = $40Y + $25Z d. Maximize profit Z = $50(Y + Z) e. Maximize profit Z = $30Y + $20Z
4 VanMetals has $3500 available for the production of new products. Wall Inc. will buy all the products they can produce.After an initial screening, VanMetals reduced the production alternatives to tables and chairs. Each table can be produced with a cost of $400. Each chair can be produced for $350.VanMetals can devote up to 100 hours to these new products; each table is expected to require 16 hours, and each chair is expected to require 8 hours. The selling prices are $600 per table and $400 per chair.VanMetals’s owner would like to use all-integer linear programming without relaxation to determine the number of tables and the number of chairs to produce to maximize revenue. What are the decision variables? What is the objective function for revenue? What are the constraints? What is the number of tables and the number of chairs to be produced to maximize revenue? What is the Maximum revenue they can expect? Draw the graphical solution of the all-integer problem. take a…
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…
RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 25 ton of material 1 and 35 of material 3. A ton of solvent base is a mixture of 12 ton of material 1, 15 ton of material 2, and 310 ton of material 3. After deducting relevant costs, the profit contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC’s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: RAW MATERIAL Amount Available for Production Material 1 20 Tons Material 2 5…
At modern woodworks, president and producer of apple crates sold to growers, has been able, with his current equipment, to produce 240 crates per 100 logs. He currently purchases 100 logs per day, and each log requires 3 labor hours to process. He believes that he can hire a profesional buyer who can buy a better quality log at the same cost. if this is the case, he can increase hos production to 260 crates per 100 logs. His labour-hours will increase by 8 hours per day. What will be the impact on productivity (measured in crates per labor-hour) if the buyer is hired?
A recently hired chief executive officer wants to reduce future production costs to improve the company's earnings, thereby increasingthe value of the company's stock. The plan is to invest $76,000 now and $58,000 in each of the next 6 years to improveproductivity. By how much must annual costs decrease in years 7 through 12 to recover the investment plus a return of 13% per year? The annual cost decreases by $....
009. from: small and medium. There are two flavors to choose from: chocolate and strawberry. There are two toppings to choose from: cherries and nuts. The tree diagram below shows the possible outcomes. Use the diagram to answer the questions. Size small medium Flavor chocolate strawberry chocolate strawberry (a) How many outcomes are there? 8 outcome(s) Topping cherries nuts cherries nuts cherries nuts cherries nuts Outcome (small, chocolate, cherries) (small, chocolate, nuts) (small, strawberry, cherries) (small, strawberry, nuts) (medium, chocolate, cherries) (medium, chocolate, nuts) (medium, strawberry, cherries) (medium, strawberry, nuts) (b) How many outcomes do not have chocolate ice cream being chosen? outcome(s) (c) How many outcomes have both strawberry ice cream and cherries being chosen? outcome(s)

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