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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
Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader–client assignments differ in terms of projected completion times. The possible
The Bahrain Manufacturing Company has orders for three similar products:Product Orders (units) A 2 000 B 500 C 1 200 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages
Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein’s customers have already placed orders that together exceed the combined capacity of Klein’s two plants. Klein’s management faces the problem of deciding how many units it should
Premier Consulting has two consultants, Avery and Baker, who can be scheduled to work for clients up to a maximum of 160 hours each over the next four weeks. A third consultant, Campbell, has some assignments already planned and is available for clients up to a maximum of 140 hours over the next
Arnoff Enterprises manufactures the central processing unit (CPU) for a line of tablet computers. The CPUs are manufactured at three sites in China: Shanghai, Changchun and Nanchang and then shipped to warehouses in Singapore, Seattle, Lisbon, Sao Paulo and Dubai for further distribution. The
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Hamilton County, 400 units; Butler County, 200 units; and Clermont County,
Consider the following network representation of a transportation problem:The supplies, demands and transportation costs per unit are shown on the network.a. Develop a linear programming model for this problem; be sure to define the variables in your model.b. Solve the linear programme to determine
a. Develop a network model of the distribution system for this problem.b. Solve the problem to determine the minimum cost shipping schedule.
A company imports goods at two ports: Lisbon and Le Havre. Shipments of one of its products are made to customers in Paris, Berlin, London and Milan. For the next planning period, the supplies at each port, customer demands and the shipping costs (E) per case from each port to each customer are as
Interpret and explain the management information provided in such solutions
Formulate and solve transhipment problems
Formulate and solve assignment problems
Formulate and solve transportation problems
Consider the linear programme: Max 3x+2x s.t. 1x1 +228 2x + 1x2 10 X1, X2 0a. Solve this problem using the Simplex method. Keep a record of the value of the objective function at each extreme point.b. Formulate and solve the dual of this problem using the graphical procedure.c. Compute the value of
Photo Chemicals produces two types of photograph-developing fluids at a cost of 1.00 per litre. Let: Xitre of product 1 X2 litre of product 2
Write the following primal problem in canonical form, and find its dual. Max 3x+1x+5x+3x+ 5.1. 3x + 1x+2x = 30 2x1+1x2+3x+1x4 15 2 +325 X1, X2, X3, X4 20
Find the dual for the following linear programme: Min 2800x + 6000x2 +1200x3 S.L. 15x+15x+ 4x+ 12x 1x3 5 8x 25 + Bxa 24 XXX 20
c. Use the dual variables to identify the machine or machines that are producing at maximum capacity. If the manager can select one machine for additional production capacity, which machine should have priority? Why?
Suppose that in a product-mix problem x1, x2, x3 and x, indicate the units of products 1,2,3 and 4, respectively, and we have: s.t 4x+6x+3x+1x4 1.5x+2x+4x+3x4 S 550 Machine A hours 4x1+1x+2x+1x4 5 700 Machine B hours 2x+3x+1x+2x200 Machine C hours X1, X2, X3, X4 20a. Formulate the dual to this
According to Innis's risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3; the higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client
Innis Investments manages funds for a number of companies and wealthy clients. For a new client, Innis has been authorized to invest up to 1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs 50 and provides an annual rate of return of 10%;
The following are additional conditions encountered by GulfGolf (Problem 6).a. Suppose because of some new machinery the company was able to make a small reduction in the amount of time it took to do the cutting and dyeing (constraint 1) for a standard bag. What effect would this reduction have on
For Problem 6:a. How much would profit increase if an additional 30 hours became available in the cutting and dyeing department (ie., ifb, were increased from 630 to 660)?b. How much would profit decrease if 40 hours were removed from the sewing department?c. How much would profit decrease it,
a. Calculate the final simplex tableau for Problem 6 after increasing b from 630 to 682*1.b. Would the current basis be optimal if b were increased further? If not, what would be the new optimal basis?
For Problem 6:a. Calculate the range of feasibility for b (cutting and dyeing capacity).b. Calculate the range of feasibility for b (sewing capacity).c. Calculate the range of feasibility for bs (finishing capacity).d. Calculate the range of feasibility forb. (inspection and packaging capacity).e.
The linear programme for this problem is: Max 10x1 þ 9x2 s:t: 0:7x1 þ 1x2 630 Cutting and dyeing time 0:5x1 þ 0:8333x2 600 Sewing time 1x1 þ 0:6667x2 708 Finishing time 0:1x1 þ 0:25x2 135 Inspection and packaging time x1; x2 0 where: x1 ¼ number of standard bags produced x2 ¼
Recall the GulfGolf problem introduced in Chapter
The linear programme for this problem is: where: Max 10x+9x2 8.1. 0.7x: + 1x2 630 Cutting and dyeing time 0.5x +0.8333x600 Sewing time 1x: +0.6667x2708 Finishing time 0.1x, + 0.25% 135 X1, X220 Inspection and packaging time x = number of standard bags produced X = number of deluxe bags produced The
For the HighTech problem, we found the range of feasibility forb, the assembly time available (see Section 6.1).a. Find the range of feasibility forb. b. Find the range of feasibility for by.c. How much will HighTech's profit increase if there is a 20-square-metre increase in the amount of
a. Find the range of feasibility forb. b. Find the range of feasibility forb. c. Find the range of feasibility for bs.
Refer again to the problem formulation and optimal simplex tableau given in Problem
Find the new optimal solution and its value.
Find the new optimal solution and its value.e. Suppose the right-hand side of the first constraint is decreased from 120 to
a. Find the dual price for the first constraint.b. Find the dual price for the second constraint.c. Find the dual price for the third constraint.d. Suppose the right-hand side of the first constraint is increased from 120 to
Refer to the problem formulation and optimal simplex tableau given in Problem
For the HighTech problem, we found the range of optimality for c1, the profit contribution per unit of the Deskpro. The final simplex tableau is given in Section 6.1. Find the following:a. The range of optimality for c2.b. The range of optimality for cs2 .c. The range of optimality for cs3 .d.
Consider the following linear programming problem. Max 5x1 þ 6x2 þ 4x3 s:t: 3x1 þ 4x2 þ 2x3 120 x1 þ 2x2 þ x3 50 x1 þ 2x2 þ 3x3 30 x1; x2; x3 0 The optimal simplex tableau is: x1 x2 x3 s1 s2 s3 Basis cB 5 6 4 0 00 s3 00 4 0 2 71 80 x3 40 2 1 1 30 30 x1 5 1 0 01 2 0 20 zj 5 8 4 1
Interpret the dual problem and solution.
Formulate the dual problem.
Complete sensitivity analysis using the information in the simplex tableau.
st Max 2x+1x2 + 1xg 4x+2x+2x24 2x+4x2
Min 1x+1x2 6.1. 8x+6x224 4x+6x-12 2x22 4
Min 3x + 32 s.t. 2x +0.5% 10 2x1 4 4x + 4x2 32 X1, X220
Max 4x+8x2 s.t 2x+2x 10 - 1x + 1x2 8 18 X1, X220
Uforia sells exclusively through department stores and employs a three-person sales staff to call on its customers. The amount of time necessary for each sales representative to sell one case of each product varies with experience and ability. Data on the average time for each of Uforia's three
Uforia Corporation sells two brands of perfume: Incentive and Temptation No.
The Our-Bags-Don't-Break (OBDB) plastic bag company manufactures three plastic refuse bags for home use: a 20 litre garbage bag, a 30 litre garbage bag and a 33 litre leaf-and- grass bag. Using purchased plastic material, three operations are required to produce each end product: cutting, sealing
Solve the following linear programme: Min 3x+4x+8x3 s.t. 4x1 +2x2 12 4x+8x316 X1, X2, X3 20
Set up the tableau form for the following linear programme (do not attempt to solve): Min 4x+5x+3x 8.1. + 2x3 20 1x2-1x35-8 401 1x-2x --5 2x + 1x2 + 1x 12 XXX 20
Set up the tableau form for the following linear programme (do not attempt to solve): Max 4x+2x-3x+5x 2x-1x+1x+2x50 3x 1x + 1x2 - 1x + 2x480 +1x4=60 X1, X2, X3, X4 20
Liva's Lumber manufactures three types of plywood. The following table summarizes the production hours per unit in each of three production operations and other data for the problem. Plywood 1 Operations (hours) Profit/Unit Grade A 2 Grade B 5 Grade X 10 422 253 40 30 2 20 Maximum time available
Suppose a company manufactures three products from two raw materials. The amount of raw material in each unit of each product is given. Raw Material Product A Product B Product C 7 kilos 6 kilos 3 kilos 5 kilos 4 kilos 2 kilos If the company has available 100 kilos of material I and 200 kilos of
Solve the RMC problem (Chapter 2, Problem 12) using the Simplex method. At each iteration, locate the basic feasible solution found by the Simplex method on the graph of the feasible region. The problem formulation is shown here: Max 40x+30x2 8.1. 0.4x1 +0.5x220 Material 1 0.2% 5 Material 2
Recall the problem for GulfGolf introduced in Section 2.1. The mathematical model for this problem is restated as follows: where Max 10x+ St. 0.7x+ 9x2 1x 630 Cutting and sewing 0.5x1 +0.8333x2 600 Sewing 1x1 +0.6667x 708 Finishing 0.1x1 + 0.25% 135 Inspection and packaging X1, X20 x = number of
Solve the following linear programme using the graphical approach: Max 4x, +5x s.t. 2x+2x 20 3x+7x2
How many units of the entering variable will be in the next solution? Before making this first iteration, what do you think will be the value of the objective function after the first iteration? g. Find the optimal solution using the Simplex method.
The following partial initial simplex tableau is given: x1 x2 x3 s1 s2 s3 Basis cB 5 20 25 0 0 0 2 1 0 1 00 40 0 2 1 0 10 30 3 0 0.5 0 0 1 15 zj cj – zja. Complete the initial tableau.b. Write the problem in tableau form.c. What is the initial basis? Does this basis correspond to the origin?
A partially completed initial simplex tableau is given:x1 x2 s1 s2 Basis cB 5 9 00 s1 0 10 9 10 90 s2 0 5 3 01 15 zj cj – zja. Complete the initial tableau.b. Which variable would be brought into solution at the first iteration?c. Write the original linear programme.
Consider the following linear programming problem: Max 60x, +90x2 3.1. 15x+45x590 5x + 5x2
Use the graphical approach to identify the solutions found in parts (c) and (d). Do the graphical results agree with your answer to part (e)? Explain.
Consider the following linear programme: Max 5x +9x2 5.1. 0.5x+1x28 1x+ 1x 10 0.25x: +1.5x 26 X1.20a. Write the problem in standard form.b. How many variables will be set equal to zero in a basic solution for this problem? Explain.c. Find the basic solution that corresponds to s, and s equal to
Consider the following linear programme: Max x1 þ 2x2 s:t: x1 þ 5x2 10 2x1 þ 6x2 16 x1; x2 0a. Write the problem in standard form.b. How many variables will be set equal to zero in a basic solution for this problem?c. Find all the basic solutions, and indicate which are also feasible.d.
d. Which of the preceding solutions would be basic feasible solutions for a linear programme?
c. Find the basic solution with x3 ¼
b. Find the basic solution with x2 ¼
Consider the following system of linear equations: 3x1 þ x2 ¼ 6 2x1 þ 4x2 þ x3 ¼ 12a. Find the basic solution with x1 ¼
Interpret the information in a Simplex tableau.
Find the optimum solution using the Simplex method.
Calculate the Simplex tableau.
Formulate an LP problem using the Simplex method.
Cinergy has learned from its trading group that Cinergy can sell 50 000 megawatt-hours of electricity over the grid (to other electricity suppliers) at a price of $30 per megawatt-hour. Should Cinergy sell the electricity? If so, which generating units should produce the additional electricity?
Suppose that Cinergy learns that the energy content of the coal from Cyprus Amax is actually 13 000 BTUs per pound. Should Cinergy revise its procurement plan?
Suppose that Cinergy can purchase an additional 80 000 tons of coal from American Coal Sales as an ‘all or nothing deal’ for $30 per ton. Should Cinergy purchase the additional 80 000 tons of coal?
Compute the average number of BTUs per pound of coal received at each generating unit (a measure of the energy efficiency of the coal received at each unit).
Compute the average cost of coal in cents per million BTUs for each generating unit (a measure of the cost of fuel for the generating units).
Determine how much coal to purchase from each of the mining companies and how it should be allocated to the generating units. What is the cost to purchase, deliver and process the coal?
Suppose that the hospital hired ten full-time nurses at the beginning of January in order to satisfy part of the requirements over the next six months. If the hospital can hire full-time nurses for E16.50 per hour, including fringe benefits, what effect would it have on total labour and training
If the cost to train each temporary nurse could be reduced to E700 per month, what effect would this change have on the hiring plan? Explain. Discuss the implications that this effect on the hiring plan has for identifying methods for reducing training costs. How much of a reduction in training
A summary table that shows the number of temporary nurses that the hospital should hire under each contract option, the associated contract cost for each option, and the associated training cost for each option. Provide summary totals showing the total number of temporary nurses hired, total
A schedule that shows the number of temporary nurses that the hospital should hire each month for each contract option.
A discussion of how the objective of minimizing total costs would provide a different model than the objective of maximizing total profit contribution. (How would the interpretation of the objective coefficients ranges differ for these two models? ).
A discussion of the objective coefficients ranges.
A discussion of the value of additional loom time (The mill is considering purchasing a ninth dobbie loom. What is your estimate of the monthly profit contribution of this additional loom? ).
The projected total contribution to profit.
The final production schedule and loom assignments for each fabric.
Recommendations regarding the hiring and training plan that will minimize the salary and training costs over the February through August period as well as answers to these questions: What is the total cost of providing technical support for the new laptop models? How much higher will monthly
The incremental salary and training cost associated with putting a current employee through the training programme. (Don’t forget that a replacement must be hired when the current employee enters the programme.)
The incremental salary and training cost associated with hiring a new employee and training him/her to be a laptop specialist.
What is your recommendation for the advertising campaign?
After reviewing HJ’s recommendation, the restaurant’s management team asked how the recommendation would change if the objective of the advertising campaign was to maximize the number of potential new customers reached. Develop the media schedule under this objective. 5 Compare the
A discussion of the ranges for the objective function coefficients. What do the ranges indicate about how sensitive the recommended solution is to HJ’s exposure rating coefficients?
How would the total exposure change if an additional R10 000 were added to the advertising budget?
A schedule showing the recommended number of television, Internet and newspaper advertisements and the budget allocation for each media. Show the total exposure and indicate the total number of potential new customers reached.
a. Because of scheduling conflicts in other markets, suppose that Leisure Air is only able to obtain one Boeing 757–200. Should the larger plane be based in Glasgow or in Edinburgh? Explain.b. Based upon your answer in part (a), determine a new allocation for the ODIFs. Briefly summarize the
Reconsider the Leisure Air problem from Section 4.5. The demand forecasts shown in Table 4.16 represent Leisure Air’s best estimates of demand. But, because demand cannot be forecasted perfectly, the number of seats actually sold for each origin-destinationitinerary fare (ODIF) may turn out to
The Quick and Easy operates five fast-food restaurants in the UK. Input measures for the restaurants include weekly hours of operation, full-time equivalent staff and weekly supply expenses. Output measures of performance include average weekly contribution to profit, market share and annual growth
Western Family Restaurant offers a variety of low-cost meals and quick service. Other than management, the restaurant operates with two full-time employees who work eight hours per day. The rest of the employees are part-time employees who are scheduled for fourhour shifts during peak meal times.
EZ-Windows manufactures replacement windows for the home renovation business. In January, the company produced 15 000 windows and ended the month with 9000 windows in inventory. EZ-Windows management team would like to develop a production schedule for the next three months. A smooth production
Jansson Cabinets received a contract to produce loud speaker cabinets for a major hi-fi manufacturer. The contract calls for the production of 3300 bookshelf speakers and 4100 floor speakers over the next two months, with the following delivery schedule.Model Month 1 Month 2 Bookshelf 2 100 1 200
Filtron Corporation produces filtration containers used in water treatment systems. Although business has been growing, the demand each month varies considerably. As a result, the company utilizes a mix of part-time and full-time employees to meet production demands. Although this approach provides
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