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operations research an introduction
Operations Research: An Introduction 10th Global Edition Hamdy A Taha - Solutions
Cars are shipped from three distribution centers to five dealers. The shipping cost is based on the mileage between the sources and the destinations and is independent of whether the truck makes the trip with partial or full loads. Table 5.28 summarizes the mileage between the distribution centers
Three orchards supply crates of oranges to four retailers. The daily demand amounts at the four retailers are 150, 150, 400, and 100 crates, respectively. Supplies at the three orchards are dictated by available regular labor and are estimated at 150, 200, and 250 crates daily. However, both
In Problem 5-8, suppose that the daily demand at area 3 drops to 4 million gallons.Surplus production at refineries 1 and 2 is diverted to other distribution areas by truck.The transportation cost per 100 gallons is $1.50 from refinery 1 and $2.20 from refinery 2.Refinery 3 can divert its surplus
In Problem 5-8, suppose that the capacity of refinery 3 is 6 million gallons only and that distribution area 1 must receive all its demand. Additionally, any shortages at areas 2 and 3 will incur a penalty of 5 cents per gallon.(a) Formulate the problem as a transportation model.(b) Determine the
Three refineries with daily capacities of 6, 5, and 8 million gallons, respectively, supply three distribution areas with daily demands of 4, 8, and 7 million gallons, respectively.Gasoline is transported to the three distribution areas through a network of pipelines.The transportation cost is 10
Solve Problem 5-6, assuming that there is a 10% power transmission loss through the network.
Three electric power plants with capacities of 25, 40, and 30 million kWh supply electricity to three cities. The maximum demands at the three cities are estimated at 30, 35, and 25 million kWh. The price per million kWh at the three cities is given in Table 5.25.During the month of August, there
In Example 5.1-2, suppose that for the case where the demand exceeds the supply(Table 5.4), a penalty is levied at the rate of $300 and $190 for each undelivered car at Denver and Miami, respectively. Additionally, no deliveries are made from the Los Angeles plant to the Miami distribution center.
In Table 5.4 of Example 5.1-2, where a dummy plant is added, what does the solution mean when the dummy plant “ships” 150 cars to Denver and 50 cars to Miami?*5-4. In Table 5.5 of Example 5.1-2, where a dummy destination is added, suppose that the Detroit plant must ship out all its production.
In each of the following cases, determine whether a dummy source or a dummy destination must be added to balance the model.(a) Supply: a1 = 100, a2 = 50, a3 = 40, a4 = 60 Demand: b1 = 100, b2 = 50, b3 = 70, b4 = 90(b) Supply: a1 = 15, a2 = 44 Demand: b1 = 25, b2 = 15, b3 = 10
True or False?(a) To balance a transportation model, it is necessary to add a dummy source or a dummy destination bur never both.(b) The amounts shipped to a dummy destination represent surplus at the shipping source.(c) The amounts shipped from a dummy source represent shortages at the receiving
In the Reddy Mikks model, the company is considering the production of a cheaper brand of exterior paint whose input requirements per ton include .75 ton of each of raw materials M1 and M2. Market conditions still dictate that the excess of interior paint over the production of both types of
In the TOYCO model, suppose that a new toy (fire engine) requires 3, 2, and 4 minutes, respectively, on operations 1, 2, and 3. Determine the optimal solution when the revenue per unit is given by*(a) $5. (b) $10.
In the TOYCO model, suppose that the company can reduce the unit times on operations 1, 2, and 3 for toy trains from the current levels of 1, 3, and 1 minutes to .5, 1, and .5 minutes, respectively. The revenue per unit is changed to $4. Determine the new optimum solution.
In the original TOYCO model, toy trains are not part of the optimal product mix. The company recognizes that market competition will not allow raising the unit price of the toy. Instead, the company wants to concentrate on improving the assembly operation itself. This entails reducing the assembly
Show that the 100% optimality rule (Problem 3-88, Chapter 3) is derived from 1reduced costs2 Ú 0 for maximization problems and 1reduced costs2 … 0 for minimization problems.
Investigate the optimality of the Reddy Mikks solution (Example 4.3-1) for each of the following objective functions. If necessary, use post-optimal analysis to determine the new optimum. (The optimal tableau of the model is given in Example 3.3-1.)*(a) z = 3x1 + 2x2(b) z = 8x1 + 10x2*(c) z = 2x1 +
Investigate the optimality of the TOYCO solution for each of the following objective functions. Where necessary, use post-optimal analysis to determine the new optimum.(The optimum tableau of TOYCO is given at the start of Section 4.5.)(a) z = 4x1 + 2x2 + 8x3(b) z = 3x1 + 6x2 + x3(c) z = 16x1 + 6x2
Secondary Constraints. Instead of solving a problem using all of its constraints, we can start by identifying the so-called secondary constraints. These are the constraints that we suspect are least restrictive in terms of the optimum solution. The model is solved using the remaining (primary)
In the TOYCO model, suppose the fourth operation has the following specifications: The maximum production rate based on 480 minutes a day is 120 units of product 1, 480 units of product 2, or 240 units of product 3. Determine the optimal solution, assuming that the daily capacity is limited to*(a)
Post-Optimal Analysis for Cases Affecting Both Optimality and Feasibility. Suppose that you are given the following simultaneous changes in the Reddy Mikks model:The revenue per ton of exterior and interior paints are $2000 and $5000, respectively, and the maximum daily availabilities of raw
Show that the 100% feasibility rule in Problem 3-79 (Chapter 3) is based on the condition aOptimum inverse b a Original right@hand side vector b Ú 0
The Ozark Farm has 20,000 broilers that are fed for 8 weeks before being marketed.The weekly feed per broiler varies according to the following schedule:Week 1 2 3 4 5 6 7 8 lb/broiler .26 .48 .75 1.00 1.30 1.60 1.90 2.10 For the broiler to reach a desired weight gain in 8 weeks, the feedstuffs
Consider the Reddy Mikks model of Example 2.1-1. Its optimal tableau is given in Example 3.3-1. If the daily availabilities of raw materials M1 and M2 are increased to 35 and 10 tons, respectively, use post-optimal analysis to determine the new optimal solution.
Suppose that TOYCO wants to change the capacities of the three operations according to the following cases:(a) °460 500 400¢ (b) °500 400 600¢ (c) °300 800 200¢ (d) °450 700 350¢Use post-optimal analysis to determine the optimum solution in each case.
In the TOYCO model listed at the start of Section 4.5, would it be more advantageous to assign the 20-minute excess capacity of operation 3 to operation 2 instead of operation 1?
The LP model of Problem 4-38(d) has no bounded solution. Show how this condition is detected by the generalized simplex procedure.
The LP model of Problem 4-38(c) has no feasible solution. Show how this condition is detected by the generalized simplex procedure.
Solve the following LP in three different ways (use TORA for convenience). Which method appears to be the most efficient computationally?Minimize z = 6x1 + 7x2 + 3x3 + 5x4 subject to 5x1 + 6x2 - 3x3 + 4x4 Ú 12 x2 - 5x3 - 6x4 Ú 10 2x1 + 5x2 + x3 + x4 Ú 8 x1, x2, x3, x4 Ú 0
Using the artificial constraint procedure introduced in Problem 4-37, solve the following problems by the dual simplex method. In each case, indicate whether the resulting solution is feasible, infeasible, or unbounded.(a) Maximize z = 2x3 subject to-x1 + 2x2 - 2x3 Ú 4-x1 + x2 + x3 … 2 2x1 - x2
Dual Simplex with Artificial Constraints. Consider the following problem:Maximize z = 2x1 - x2 + x3 subject to 2x1 + 3x2 - 5x3 Ú 4 -x1 + 9x2 - x3 Ú 3 4x1 + 6x2 + 3x3 … 8 x1, x2, x3 Ú 0 The starting basic solution consisting of surplus variables x4 and x5 and slack variable x6 is infeasible
Generate the dual simplex iterations for the following problems (using TORA for convenience), and trace the path of the algorithm on the graphical solution space.(a) Minimize z = 2x1 + 3x2 subject to 2x1 + 2x2 … 3 x1 + 2x2 Ú 1 x1, x2 Ú 0(b) Minimize z = 5x1 + 6x2 subject to x1 + x2 Ú 20 4x1 +
Consider the solution space in Figure 4.3, where it is desired to find the optimum extreme point that uses the dual simplex method to minimize z = 2x1 + x2. The optimal solution occurs at point F = 10.5, 1.52 on the graph.(a) Can the dual simplex start at point A?*(b) If the starting basic
The company estimates that for each part that is not produced (per the optimum solution), an across-the-board 20%reduction in machining time can be realized through process improvements. Would these improvements make these parts profitable? If not, what is the minimum percentage reduction needed to
Consider the optimal solution of JoShop in Problem
JoShop uses lathes and drill presses to produce four types of machine parts, PP1, PP2, PP3, and PP4. The following table summarizes the pertinent data:Machining time in minutes per unit of Machine PP1 PP2 PP3 PP4 Capacity (min)Lathes 2 5 3 4 5300 Drill presses 3 4 6 4 5300 Unit revenue ($) 3 6 5 4
In Example 4.3-2, suppose that TOYCO is studying the possibility of introducing a fourth toy: fire trucks. The assembly does not make use of operation 1. Its unit assembly times on operations 2 and 3 are 1 and 3 minutes, respectively. The revenue per unit is $4. Would you advise TOYCO to introduce
In Example 4.3-2, suppose that for toy trains the per-unit time of operation 2 can be reduced from 3 minutes to at most 1.3 minutes. By how much must the per-unit time of operation 1 be reduced to make toy trains just profitable?
BagCo produces leather jackets and handbags. A jacket requires 8 m2 of leather, and a handbag only 2 m2. The labor requirements for the two products are 12 and 5 hours, respectively. The current weekly supplies of leather and labor are limited to 600 m2 and 925 hours, respectively. The company
NWAC Electronics manufactures four types of simple cables for a defense contractor.Each cable must go through four sequential operations: splicing, soldering, sleeving, and inspection. The following table gives the pertinent data of the situation:Minutes per unit Cable Splicing Soldering Sleeving
In Example 4.3-1, compute the change in the optimal revenue in each of the following cases (use TORA output to obtain the feasibility ranges):(a) The constraint for raw material M1 (resource 1) is 6x1 + 4x2 … 20.(b) The constraint for raw material M2 (resource 2) is x1 + 2x2 … 5.(c) The market
Show that Method 1 in Section 4.2.3 for determining the optimal dual values is actually based on the Formula 2 in Section 4.2.4.
Consider the following LP:Maximize z = 2x1 + 4x2 + 4x3 - 3x4 subject to x1 + x2 + x3 = 4 x1 + 4x2 + x4 = 8 x1, x2, x3, x4 Ú 0 Use the dual problem to show that the basic solution (x1, x2) is not optimal.
The following is the optimal tableau for a maximization LP model with three (…)constraints and all nonnegative variables. The variables x3, x4, and x5 are the slacks associated with the three constraints. Determine the associated optimal objective value in two different ways by using the primal
Consider the following LP model:Maximize z = 5x1 + 2x2 + 3x3 subject to x1 + 5x2 + 2x3 … b1 x1 - 5x2 - 6x3 … b2 x1, x2, x3 Ú 0 The following optimal tableau corresponds to specific values of b1 and b2:Basic x1 x2 x3 x4 x5 Solution z 0 a 7 d e 15 x1 1 b 2 1 0 3 x5 0 c -8 -1 1 1 Determine the
Consider the following LP model:Maximize z = 5x1 + 12x2 + 4x3 subject to x1 + 2x2 + x3 + x4 = 5 2x1 - x2 + 3x3 = 1 x1, x2, x3, x4 Ú 0(a) Identify the best solution from among the following basic feasible solutions:(i) Basic variables = 1x4, x32, Inverse = °1 -13 0 13 ¢(ii) Basic variables = 1x2,
Consider the following LP model:Minimize z = 2x1 + x2 subject to 3x1 + x2 - x3 = 3 4x1 + 3x2 - x4 = 6 x1 + 2x2 + x5 = 3 x1, x2, x3, x4, x5 Ú 0 Compute the entire simplex tableau associated with the following basic solution, and check it for optimality and feasibility.Basic variables = 1x1, x2,
Consider the following LP model:Maximize z = 3x1 + 2x2 + 5x3 subject to x1 + 2x2 + x3 + x4 = 30 3x1 + 2x3 + x5 = 60 x1 + 4x2 + x6 = 20 x2, x2, x3, x4, x5, x6 Ú 0 Check the optimality and feasibility of the following basic solutions:(a) Basic variables = 1x4, x3, x62, Inverse = °1 -12 0 0 12 0 0 0
Consider the following LP model:Maximize z = 4x1 + 14x2 subject to 2x1 + 7x2 + x3 = 21 7x1 + 2x2 + x4 = 21 x1, x2, x3, x4 Ú 0 Check the optimality and feasibility of each of the following basic solutions:(a) Basic variables = 1x2, x42, Inverse = a 17 0-27 1b(b) Basic variables = 1x2, x32, Inverse
Generate the first simplex iteration of Example 4.2-1 (you may use TORA’s Iterations 1 M@method with M = 100 for convenience), then use Formulas 1 and 2 to verify all the elements of the resulting tableau.
In Problem 4-17(a), let y1 and y2 be the dual variables. Determine whether the following pairs of primal–dual solutions are optimal:*(a) (x1 = 3, x2 = 1; y1 = 4, y2 = 1)(b) (x1 = 4, x2 = 1; y1 = 1, y2 = 0)(c) (x1 = 3, x2 = 0; y1 = 5, y2 = 0)
Estimate a range for the optimal objective value for the following LPs:*(a) Minimize z = 5x1 + 2x2 subject to x1 - x2 Ú 3 2x1 + 3x2 Ú 5 x1, x2 Ú 0(b) Maximize z = x1 + 5x2 + 3x3 subject to x1 + 2x2 + x3 = 30 2x1 - x2 = 40 x1, x2, x3 Ú 0(c) Maximize z = 2x1 + x2 subject to x1 - x2 … 2 2x1 …
Consider the following set of inequalities:2x1 + 3x2 … 12-3x1 + 2x2 … -4 3x1 - 5x2 … 2 x1 unrestricted x2 Ú 0 A feasible solution can be found by augmenting the trivial objective function, maximize z = x1 + x2, and then solving the problem. Another way is to solve the dual, from which a
Consider the following LP:Maximize z = x1 + 5x2 + 3x3 subject to x1 + 2x2 + x3 = 3 2x1 - x2 = 4 x1, x2, x3 Ú 0 The starting solution consists of x3 in the first constraint and an artificial x4 in the second constraint with M = 100. The optimal tableau is given as Basic x1 x2 x3 x4 Solution z 0 2 0
Consider the following LP:Maximize z = 2x1 + 4x2 + 4x3 - 3x4 subject to x1 + x2 + x3 = 4 x1 + 4x2 + x4 = 8 x1, x2, x3, x4 Ú 0 Using x3 and x4 as starting variables, the optimal tableau is given as Basic x1 x2 x3 x4 Solution z 2 0 0 3 16 x3 .75 0 1 -.25 2 x2 .25 1 0 .25 2 Write the associated dual
Consider the following LP:Minimize z = 4x1 + x2 subject to 3x1 + x2 = 30 4x1 + 3x2 Ú 60 x1 + 2x2 … 40 x1, x2 Ú 0 The starting solution consists of artificial x4 and x5 for the first and second constraints and slack x6 for the third constraint. Using M = 100 for the artificial variables, the
Consider the following LP:Maximize z = 5x1 + 2x2 + 3x3 subject to x1 + 5x2 + 2x3 = 15 x1 - 5x2 - 6x3 … 20 x1, x2, x3 Ú 0 Given that the artificial variable x4 and the slack variable x5 form the starting basic variables and that M was set equal to 100 when solving the problem, the optimal tableau
Solve the dual of the following problem, and then find its optimal solution from the solution of the dual. Does the solution of the dual offer computational advantages over solving the primal directly?Minimize z = 50x1 + 60x2 + 30x3 subject to 5x1 + 5x2 + 3x3 Ú 50 x1 + x2 - x3 Ú 20 7x1 + 6x2 -
Find the optimal value of the objective function for the following problem by inspecting only its dual. (Do not solve the dual by the simplex method.)Minimize z = 10x1 + 4x2 + 5x3 subject to 5x1 - 7x2 + 3x3 Ú 20 x1, x2, x3 Ú 0
Repeat Problem 4-8 for the last tableau of Example 3.4-2.
Consider the optimal tableau of Example 3.3-1.*(a) Identify the optimal inverse matrix.(b) Show that the right-hand side equals the inverse multiplied by the original right-hand side vector of the original constraints.
Consider the following matrices:a = £1 4 2 5 3 6 , p1 = a 10 20b, p2 = £10 20 30 V1 = 111, 222, V2 = 1 -2, -4, -62 In each of the following cases, indicate whether the given matrix operation is legitimate, and, if so, calculate the result.*(a) aV1(b) ap1(c) ap2 (d) V1a *(e) V2a (f) p1p 2 (g) V1p1
True or False?(a) The dual of the dual problem yields the original primal.(b) If the primal constraint is originally in equation form, the corresponding dual variable is necessarily unrestricted.(c) If the primal constraint is of the type …, the corresponding dual variable will be nonnegative
Consider Example 4.1-1. The application of the simplex method to the primal requires the use of an artificial variable in the second constraint of the standard primal to secure a starting basic solution. Show that the presence of an artificial primal in equation form variable does not affect the
Write the dual for each of the following primal problems:(a) Maximize z = 66x1 - 22x2 subject to-x1 + x2 … -2 2x1 + 3x2 … 5 x1, x2 Ú 0(b) Minimize z = 6x1 + 3x2 subject to 6x1 - 3x2 + x3 Ú 25 3x1 + 4x2 + x3 Ú 55 x1, x2, x3 Ú 0(c) Maximize z = x1 + x2 subject to 2x1 + x2 = 5 3x1 - x2 = 6 x1,
In Example 4.1-3, show that even if the sense of optimization in the primal is changed to minimization, an unrestricted primal variable always corresponds to an equality dual constraint.
In Example 4.1-2, derive the associated dual problem given that the primal problem is augmented with a third constraint, 3x1 + x2 = 4.
In Example 4.1-1, derive the associated dual problem if the sense of optimization in the primal problem is changed to minimization.
Consider Problem 2-76 (Chapter 2).(a) Which of the specification constraints impacts the optimum solution adversely?(b) Is it economical for the company to purchase ore 1 at $100/ton. Explain in terms of dual prices.
Consider Problem 2-49, (Chapter 2).(a) Suppose that the manufacturer can purchase additional units of raw material A at$12 per unit. Would it be advisable to do so?(b) Would you recommend that the manufacturer purchase additional units of raw material B at $5 per unit?
Consider Problem 2-48, (Chapter 2). Suppose that any additional capacity of machines 1 and 2 can be acquired only by using overtime. What is the maximum cost per hour the company should be willing to incur for either machine?
Consider Problem 2-47, (Chapter 2). Relate the dual prices to the unit production costs of the model.
Consider Problem 2-45 (Chapter 2). Use the dual price to decide if it is advisable for the gambler to bet an additional $400.
Consider Problem 2-44, (Chapter 2). Use the dual price to determine if it is worthwhile for the executive to invest more money in the plans.
Consider Problem 2-43, (Chapter 2). Use the dual prices to determine the rate of return associated with each year.
Consider Problem 2-42 (Chapter 2).(a) Give an economic interpretation of the dual prices of the model.(b) Show how the dual price associated with the upper bound on borrowed money at the beginning of the third quarter can be derived from the dual prices associated with the balance equations
Consider Problem 2-41 (Chapter 2).(a) Use the dual prices to determine the overall return on investment.(b) If you wish to spend $2000 on pleasure at the end of year 1, how would this affect the accumulated amount at the start of year 5?
Consider Problem 2-40 (Chapter 2). Use the dual price to decide if it is worthwhile to increase the funding for year 4.22
The 100% Optimality Rule. A rule similar to the 100% feasibility rule outlined in Problem 3-79, can also be developed for testing the effect of simultaneously changing all cj to cj + dj, j = 1, 2,c, n, on the optimality of the current solution. Suppose that uj … dj … vj is the optimality range
Dean’s Furniture Company assembles regular and deluxe kitchen cabinets from precut lumber. The regular cabinets are painted white, and the deluxe are varnished. Both painting and varnishing are carried out in one department. The daily capacity of the assembly department is 400 regular cabinets
Popeye Canning is contracted to receive daily 50,000 lb of ripe tomatoes at 7 cents per pound, from which it produces canned tomato juice, tomato sauce, and tomato paste. The canned products are packaged in 24-can cases. A can of juice uses 1 lb of fresh tomatoes, a can of sauce uses 12 lb, and a
Electra produces four types of electric motors, each on a separate assembly line. The respective capacities of the lines are 500, 500, 800, and 750 motors per day. Type 1 motor uses 8 units of a certain electronic component, type 2 motor uses 5 units, type 3 motor uses 4 units, and type 4 motor
The Bank of Elkins is allocating a maximum of $200,000 for personal and car loans during the next month. The bank charges 14% for personal loans and 12% for car loans.Both types of loans are repaid at the end of a 1-year period. Experience shows that about 3% of personal loans and 2% of car loans
Baba Furniture Company employs four carpenters for 10 days to assemble tables and chairs. It takes 2 person-hours to assemble a table and half a person-hour to assemble a chair. Customers usually buy one table and four to six chairs. The prices are $135 per table and $50 per chair. The company
B&K grocery store sells three types of soft drinks: the brand names A1 Cola, A2 Cola, and the cheaper store brand BK Cola. The price per can for A1, A2, and BK are 80, 70, and 60 cents, respectively. On the average, the store sells no more than 500 cans of all colas a day. Although A1 is a
In the TOYCO model, determine if the current solution will change in each of the following cases:21(i) z = x1 + x2 + 4x3(ii) z = 4x1 + 6x2 + x3(iii) z = 6x1 + 3x2 + 9x3
Consider the problem Maximize z = x1 + x2 subject to 2x1 + x2 … 6 x1 + 2x2 … 6 x1 + x2 Ú 0(a) Show that the optimal basic solution includes both x1 and x2 and that the feasibility ranges for the two constraints, considered one at a time, are -3 … D1 … 6 and-3 … D2 … 6.*(b) Suppose that
The 100% feasibility rule. A simplified rule based on the individual changes D1, D2, . . . , and Dm in the right-hand side of the constraints can be used to test whether or not simultaneous changes will maintain the feasibility of the current solution. Assume that the right-hand side bi of
HiDec produces two models of electronic gadgets that use resistors, capacitors, and chips.The following table summarizes the data of the situation:Unit resource requirements Resource Model 1 (units) Model 2 (units) Maximum availability (units)Resistor 2 3 1200 Capacitor 2 1 1000 Chips 0 4 800 Unit
The Gutchi Company manufactures purses, shaving bags, and backpacks. The construction of the three products requires leather and synthetics, with leather being the limiting raw material. The production process uses two types of skilled labor: sewing and finishing.The following table gives the
An assembly line consisting of three consecutive workstations produces two radio models: DiGi-1 and DiGi-2. The following table provides the assembly times for the three workstations.Minutes per unit Workstation DiGi-1 DiGi-2 1 6 4 2 5 4 3 4 6 The daily maintenance for workstations 1, 2, and 3
ChemLabs uses raw materials I and II to produce two domestic cleaning solutions, A and B. The daily availabilities of raw materials I and II are 150 and 145 units, respectively.One unit of solution A consumes .5 unit of raw material I and .6 unit of raw material II, and one unit of solution B uses
The Burroughs Garment Company manufactures men’s shirts and women’s blouses for Walmark Discount Stores. Walmark will accept all the production supplied by Burroughs.The production process includes cutting, sewing, and packaging. Burroughs employs 25 workers in the cutting department, 35 in the
Show & Sell can advertise its products on local radio and television (TV), or in newspapers.The advertising budget is limited to $10,000 a month. Each minute of advertising on radio costs $15 and each minute on TV costs $300. A newspaper ad costs $50. Show &Sell likes to advertise on radio at least
The Continuing Education Division at the Ozark Community College offers a total of 30 courses each semester. The courses offered are usually of two types: practical, such as woodworking, word processing, and car maintenance, and humanistic, such as history, music, and fine arts. To satisfy the
A company that operates 10 hrs a day manufactures three products on three processes.The following table summarizes the data of the problem:Minutes per unit Product Process 1 Process 2 Process 3 Unit price 1 10 6 8 $4.50 2 5 8 10 $5.00 3 6 9 12 $4.00(a) Determine the optimal product mix.(b) Use the
A company produces three products, A, B, and C. The sales volume for A is at least 50%of the total sales of all three products. However, the company cannot sell more than 80 units of A per day. The three products use one raw material, of which the maximum daily availability is 240 lb. The usage
Consider the TOYCO model.(a) Suppose that any additional time for operation 1 beyond its current capacity of 430 mins per day must be done on an overtime basis at $50 an hour. The hourly cost includes both labor and the operation of the machine. Is it economically advantageous to use overtime with
In the TOYCO model, suppose that the changes D1, D2, and D3 are made simultaneously in the three operations.20(a) If the availabilities of operations 1, 2, and 3 are changed to 440, 490, and 400 minutes, respectively, use the simultaneous conditions to show that the current basic solution remains
In Problem 3-64:(a) Determine the optimality range for the unit revenue ratio of the two types of hats that will keep the current optimum unchanged.(b) Using the information in (a), will the optimal solution change if the revenue per unit is the same for both types?
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