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Questions and Answers of
Project Managers
Maximal flow networks.
Minimal spanning tree networks.
Shortest-route networks.
The charity is discussing with its Swedish and German suppliers the possibility of them supplying some of the zones directly. Under review are the possibilities of the German supplier shipping
The company is willing to consider altering its current strategy so that any of the three distribution centres could supply any of the zones (where this is logistically feasible). Can costs be
If the charity maintains its current supply and distribution strategy, what will its supply and distribution costs be for the coming year?
Use the Hungarian method to solve the Salisbury Discount, problem by using the profit data in Table 7.27.
Using the Hungarian method, obtain the optimal solution.
Refer to Problem
Refer again to the Contois Carpets problem for which the network representation is shown in Figure 7.12. This problem can also be formulated and solved as a transportation problem.a. Develop a
Use the per-unit cost changes for each unoccupied cell shown in Table 7.10 to do the following:a. Consider the arc connecting Brazil and Dubai as a candidate for the incoming arc. Allocate 1 unit of
Consider the following minimum cost transportation problem.a. Use the minimum cost method to find an initial feasible solution.b. Use the transportation Simplex method to find an optimal solution.c.
Consider the following minimum cost transportation problem.a. Use the minimum cost method to find an initial feasible solution.b. Use the transportation Simplex method to find an optimal solution.c.
Consider the following transportation tableau with four origins and four destinations.a. Use the MODI method to determine whether this solution provides the minimum transportation cost. If it is not
The distribution system for the Herman Company consists of three plants, two warehouses and four customers. Plant capacities and shipping costs (E) from each plant to each warehouse are: Warehouse
Assume that in Problem 9 an additional employee is available for possible assignment. The following table shows the assignment alternatives and the estimated completion times. Client Project Leader 1
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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.
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