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An Introduction To Management Science Quantitative Approaches To Decision Making 2nd Edition David Ray Anderson, Dennis J. Sweeney, Thomas Arthur Williams, Mik Wisniewski - Solutions
The Silver Star Bicycle Company in India will be manufacturing both men’s and women’s models for its Easy-Pedal ten-speed bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current
The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by truck. The company recently contracted to supply gasoline distributors in southern Ohio, and it has $600 000 available to spend on the necessary expansion of its fleet of gasoline tank trucks. Three models of
Frandec Company manufactures, assembles and rebuilds material handling equipment used in warehouses and distribution centres. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports and a metal strap Frandec’s production schedule calls for 5000
Seastrand Oil Company produces two grades of fuel: regular and high octane. Both fuels are produced by blending two types of crude oil. Although both types of crude oil contain the two important ingredients required to produce both fuels, the percentage of important ingredients in each type of
Romans Food Market, located in Italy, carries a variety of speciality foods from around the world. Two of the store’s leading products use the Romans Food Market name: Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of Brazilian Natural and Colombian Mild coffee beans,
Determine the optimal buying-storing-selling strategy for ASC. What is the projected four-week profit?
The Atlantic Seafood Company (ASC) is a buyer and distributor of seafood products that are sold to restaurants and speciality seafood outlets throughout the Western Europe. ASC has a frozen storage facility in Lisbon that serves as the primary distribution point for all products. One of the ASC
A local hospital purchases two types of drug from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the hospital’s needs. In addition, the suppliers charge different prices for the drugs. Price data (in price per unit) are as follows: Supplier Drug 1
Reconsider the Welte Mutual Funds problem from Section 4.5. Define your decision variables as the fraction of funds invested in each security. Also, modify the constraints limiting investments in the oil and steel industries as follows: no more than 50 per cent of the total funds invested in stock
The North Somerset Police’s Department schedules police officers for eight-hour shifts. The start times for the shifts are 8:00 A.M., noon, 4:00 P.M., 8:00 P.M., midnight and 4:00 A.M. An officer beginning a shift at one of these times works for the next eight hours. During normal weekday
Kunz and Sons manufactures two products used in the heavy equipment industry. Both products require manufacturing operations in two departments. The following are the production time (in hours) and profit contribution figures for the two products. Labour-Hours Product Profit per Unit, E Dept. A
Ajax Fuels is developing a new additive for aeroplane fuels. The additive is a mixture of three ingredients: A, B and C. For proper performance, the total amount of additive (amount of A + amount of B + amount of C) must be at least ten grams per litre of fuel. However, because of safety reasons,
The individual ratings of the aroma and taste for coffee made from 100 per cent of each bean are as follows. Bean Aroma Rating Taste Rating 1 75 86 2 85 88 3 60 75 Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the
Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per kilo and the available kilos of each bean are as follows: Bean Cost per kilo Available kilos 1 E0.50 500 2 E0.70 600 3 E0.45 400 Consumer tests with coffee products were used to provide ratings on a
b. In calculating the profit contribution per unit, management doesn’t deduct labour costs because they are considered fixed for the upcoming planning period. However, suppose that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime?
The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labour availability, labour utilization and product profitability. Product (hours/unit) Department 1 2 Labour-Hours Available A
The Uppsala Chamber of Commerce periodically sponsors public service seminars and programmes. Currently, promotional plans are under way for this year’s programme. Advertising alternatives include television, Internet and newspaper. Audience estimates, costs and maximum media usage limitations
The individual ratings of the aroma and taste for coffee made from 100 per cent of each bean are as follows. Bean Aroma Rating Taste Rating 1 75 86 2 85 88 3 60 75 Assume that the aroma and taste attributes of the coffee blend will be a weighted average of the attributes of the beans used in the
Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per kilo and the available kilos of each bean are as follows: Bean Cost per kilo Available kilos 1 E0.50 500 2 E0.70 600 3 E0.45 400 Consumer tests with coffee products were used to provide ratings on a
b. In calculating the profit contribution per unit, management doesn’t deduct labour costs because they are considered fixed for the upcoming planning period. However, suppose that overtime can be scheduled in some of the departments. Which departments would you recommend scheduling for overtime?
The management of Hartman Company is trying to determine the amount of each of two products to produce over the coming planning period. The following information concerns labour availability, labour utilization and product profitability.Product (hours/unit) Department 1 2 Labour-Hours Available A
The Uppsala Chamber of Commerce periodically sponsors public service seminars and programmes. Currently, promotional plans are under way for this year’s programme. Advertising alternatives include television, Internet and newspaper. Audience estimates, costs and maximum media usage limitations
The investment in Pacific Oil, the high-return but high-risk investment, cannot be more than 60 per cent of the total oil industry investment.
Government bonds should be at least 25 per cent of the steel industry investments.
Neither industry (oil or steel) should receive more than E50
At least 60 per cent of the interviews for households without children must be conducted during the evening.
At least 40 per cent of the interviews for households with children must be conducted during the evening.
The total number of households interviewed during the evening must be at least as great as the number of households interviewed during the day.
Interview at least 400 households without children.
Interview at least 400 households with children.
Interpret the solutions to common LP problems
Formulate complex LP problems
Recognize common application areas for LP
The asset allocation model you developed may be useful in modifying the portfolios for all of the firm’s clients whenever the anticipated yields for the three funds are periodically revised. What is your recommendation as to whether use of this model is possible?
Assume that the client expressed some concern about having too much money in the growth fund. How would the original recommendation change if the amount invested in the growth fund is not allowed to exceed the amount invested in the income fund?
Refer again to the original situation where the client’s risk index was assessed to be 0.05. How would your investment recommendation change if the annual yield for the growth fund were revised downward to 16 per cent or even to 14 per cent?
Assume that the client’s risk index could be increased to 0.055. How much would the yield increase and how would the investment recommendation change?
Recommend how much of the E800 000 should be invested in each of the three funds. What is the annual yield you anticipate for the investment recommendation?
Recommendations on how profit contribution could be increased (if at all) if TJ’s does not satisfy all existing orders.
A recommendation as to whether TJ’s should purchase an additional 1000 kilos of almonds for E1000 from a supplier who overbought.
Recommendations regarding how the total profit contribution can be increased if additional quantities of nuts can be purchased.
The optimal product mix and the total profit contribution.
The cost per kilo of the nuts included in the Regular, Deluxe and Holiday mixes.
The programme manager for Channel 10 would like to determine the best way to allocate the time for the 11:00-11:30 evening news broadcast. Specifically, she would like to determine the number of minutes of broadcast time to devote to local news, national news, weather and sports. Over the 30-minute
Abu Dhabi Savings Bank (ADSB) has $1 million in new funds that must be allocated to home loans, personal loans and automobile loans. The annual rates of return for the three types of loans are 7 per cent for home loans, 12 per cent for personal loans and 9 per cent for automobile loans. The bank's
Round Tree Manor is a hotel that has two types of rooms with three rental classes: Super Saver, Deluxe and Business. The profit per night for each type of room and rental class is as follows: Rental Class Super Saver Deluxe Business Room Type I Type II 30 35 20 30 40 Type I rooms do not have
Would this help or hurt profit? Explain.
A maximum of 100 hours of overtime can be scheduled. Marketing requirements specify a minimum production of 100 suits and 75 sport coats. S = number of suits produced SC = number of sport coats produced D = hours of overtime for the cutting operation D2 hours of overtime for the sewing operation
For the coming week, 200 hours of cutting time, 180 hours of sewing time and 1200 metres of fabric are available. Additional cutting and sewing time can be obtained by scheduling overtime for these operations. Each hour of overtime for the cutting operation increases the hourly cost by 15, and each
Each sport coat requires 0.8 hours of cutting time and 0.6 hours of sewing time, uses four metres of material, and provides a profit contribution of
Tucker Inc. produces high-quality suits and sport coats for men. Each suit requires 1.2 hours of cutting time and 0.7 hours of sewing time, uses six metres of material, and provides a profit contribution of
Refer to the computer solution of Problem 15 in Figure 3.19.a. Interpret the ranges of optimality for the objective function coefficients.b. Suppose that the manufacturing cost increases to 11.20 per case for model A. What is the new optimal solution?c. Suppose that the manufacturing cost increases
Digital Controls, Inc. (DCI), manufactures two models of a radar speed device used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus one km per hour, whereas the smaller model B has an accuracy of plus or minus three km per hour. For the next week, the company
Refer to the computer solution of Problem 13 in Figure 3.18.a. Identify the range of optimality for each objective function coefficient.b. Suppose the profit for the economy model is increased by 6 per unit, the profit for the standard model is decreased by 2 per unit, and the profit for the deluxe
Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model and a deluxe model. The profits per unit are 63, 95 and 135, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Manufacturing Time (hours)
Letting: W jars of Western Foods Salsa M = jars of Mexico City Salsa leads to the formulation: Max 1W+1.25M s.t 104W+ 196M 280000 Whole tomatoes 84W+28M 130000 Tomato sauce 56W+56M 100000 Tomato paste W.M0 The solution is shown in Figure 3.17.a. What is the optimal solution, and what are the
Recall the Miguel's problem in Chapter 2, Problem
a. How much would the estimated per-share return for United Oil have to increase before it would be beneficial to increase the investment in this stock?b. How much would the estimated per-share return for Huber Steel have to decrease before it would be beneficial to reduce the investment in this
Refer to Figure 3.16, which shows the computer solution of Problem
In addition, the portfolio is limited to a maximum of 1000 shares of United Oil. The linear programming formation that will maximize the total annual return of the portfolio is as follows: Max 3U+ 5H Maximize total annual return s.t 25U+ 50H 80,000 Funds available 0.50U+0.25H 700 Risk maximum 1U
Investment Advisors, Inc., is a brokerage firm that manages stock portfolios for a number of clients. A particular portfolio consists of U shares of United Oil and H shares of Huber Steel. The annual return for United Oil is 3 per share and the annual return for Huber Steel is 5 per share. United
Refer to the computer solution in Figure 3.15 (see Problem 8).a. Calculate the ranges of optimality for the objective function coefficients.b. Interpret the ranges in part (a).c. Interpret the range of feasibility for the right-hand sides.d. How much will the value of the optimal solution improve
Find the new optimal solution. Recall the GulfGolf glove problem (Chapter 2, Problem 13). Letting: R = number of regular gloves P= number of professional gloves leads to the following formulation: Max 5R+ 8P s.t R+P900 Cutting and dyeing 2R+P300 Finishing /R+P 100 packaging and shipping R.P 0 The
Find the new optimal solution.b. Suppose the objective function coefficient of x, is increased to 3 and the objective function coefficient of x2 is decreased to
Ba. Suppose the objective function coefficient of x, is increased to 3 and the objective function coefficient of x2 is increased to
Calculate and interpret the dual prices for the constraints.
Refer to Problem
Consider the following linear programme: Min x1 þ x2 s:t x1 þ 2x2 7 2x1 þ x2 5 x1 þ 6x2 11 x1; x2 0a. Solve this problem using the graphical solution procedure.b. Calculate the range of optimality for the objective function coefficient of x1.c. Calculate the range of optimality for the
Calculate the dual prices for constraints 1 and 2 and interpret them.
Refer to Problem
What is the new optimal solution?
Explain the management implications of sensitivity analysis.leads to the formulation: Max 40F þ 30S s:t 2 /5F þ 1 /2 S 20 Material 1 1 /2 S 5 Material 2 3 /5F þ 3 /10 S 21 Material 3 F; S 0 Use the graphical sensitivity analysis approach to determine the range of optimality for the
Undertake graphical sensitivity analysis l Undertake sensitivity analysis using computer output.
Explain the importance of sensitivity analysis in linear programming.
Suppose that in part (1) management specified the objective of maximizing the total number of printers produced each shift rather than total profit contribution. With this objective, how many units of each printer should be produced per shift? What effect does this objective have on total profit
Management wants to limit the difference between the total time on line 1 and the total time on line 2 to 30 minutes or less. If the objective is still to maximize the total contribution to profit, how many units of each printer should be produced? What effect does this workload balancing have on
Management requested an expansion of the model in part (2) that would provide a better balance between the total time on line 1 and the total time on line.
Does the solution you developed in part (2) balance the total time spent on line 1 and the total time spent on line 2? Why might this balance or lack of it be a concern to management?
Suppose that management also states that the number of DI-910 printers produced must be at least as great as the number of DI-950 units produced. Assuming that the objective is to maximize the total contribution to profit for an eight-hour shift, how many units of each printer should be produced?
The recommended number of units of each printer to produce to maximize the total contribution to profit for an eight-hour shift. What reasons might management have for not implementing your recommendation?
Consider the following linear programme: Min 2x1 + 2x2a. show the feasible region. s.t. 1x + 3x2 12 3x1 + 1x2 13 1x11x2=3 X1, X2 0b. what are the extreme points of the feasible region?c. Find the optimal solution using the graphical solution procedure.
For the linear programme Min 6x1 + 4x2 s.t. 2x1 + 1x2 12 1x1 + 1x2 10 1x2 4 X1, X2 0a. Write the linear programme in standard form.b. Find the optimal solution using the graphical solution procedure.c. What are the values of the slack and surplus variables?
Management of High Tech Services (HTS) would like to develop a model that will help allocate their technicians’ time between service calls to regular contract customers and new customers. A maximum of 80 hours of technician time is available over the twoweek planning period. To satisfy cash flow
Does the following linear programme involve infeasibility, unbounded and/or alternative optimal solution? Explain. Max 1x1 þ 1x2 s:t: 8x1 þ 6x2 24 4x1 þ 6x2 12 2x2 4 x1; x2 0
Does the following linear programme involve infeasibility, unbounded and/or alternative optimal solutions? Explain.Max 4x1 þ 8x2 s:t: 2x1 þ 2x2 10 1x1 þ 1x2 8 x1; x2 0
As part of a quality improvement initiative, government employees complete a three-day training programme on teamwork and a two-day training programme on problem solving. The manager of quality improvement requested that at least eight training programmes on teamwork and at least ten training
Miguel’s Mexican produces various Mexican food products and sells them to Western Foods, a chain of grocery stores located in Europe. Miguel’s makes two salsa products: Western Foods Salsa and Mexico City Salsa. Essentially, the two products have different blends of whole tomatoes, tomato sauce
A local health clinic is keen to raise awareness and understanding of AIDS/HIV in the local community and has managed to attract some funding for local advertising. The clinic would like to determine the best way to allocate a monthly advertising budget of E1000 between newspaper advertising and
GulfGolf also make two different types of golfing gloves: a regular model and a professional model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department and 100 hours available in its packaging and shipping
After deducting relevant costs, the profit contribution is E40 for every kilo of fuel additive produced and E30 for every kilo 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
A kilo of solvent base is a mixture of 0.5 kilos of material 1, 0.2 kilos of material 2 and 0.3 kilos of material
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 kilo of fuel additive is a mixture of 0.4 kilos of material 1 and 0.6 kilos
Write the following linear programme in standard form: Max 5x1 þ 2x2 þ 8x3 s:t: 1x1 þ 2x2 þ 1 /2x3 420 2x1 þ 3x2 1x3 610 6x1 1x2 þ 3x3 125 x1; x2; x3 0
Refer to the GulfGolf problem described in Section 2.1. Suppose that management encounters each of the following situations:a. The accounting department revises its estimate of the profit contribution for the deluxe bag to $18 per bag.b. A new low-cost material is available for the standard bag,
Consider the following linear programme: Max 1x1 þ 2x2 s:t: 1x1 5 1x2 4 2x1 þ 2x2 ¼ 12 x1; x2 0a. Show the feasible region.b. What are the extreme points of the feasible region?c. Find the optimal solution using the graphical procedure.
Consider the following linear programme: Min 3x1 þ 4x2 s:t: 1x1 þ 3x2 6 1x1 þ 1x2 4 x1, x2 0 Identify the feasible region and find the optimal solution using the graphical solution procedure. What is the value of the objective function?
For the linear programme: Max 2x1 þ 3x2 s:t: 1x1 þ 2x2 6 5x1 þ 3x2 15 x1; x2 0 find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution?
Identify the feasible region for the following set of constraints: 1 /2x1 þ 1 /4x2 30 1x1 þ 5x2 250 1 /4x1 þ 1 /2x2 50 x1; x2 0
Three objective functions for linear programming problems are 7x1 + 10x2, 6x1 + 4x2 and 4x1 + 7x2. Determine the slope of each objective function. Show the graph of each for objective function values equal to
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