Concept explainers
a)
To determine: The way to minimize the sum of penalty and shipping cost.
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to be unfeasible solution.
b)
To determine: The way the change in penalty cost affects the optimal cost.
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints then it is said to be unfeasible solution.
c)
To determine: The way the change in warehouse capacity affects the optimal cost.
Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to be unfeasible solution.
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Chapter 5 Solutions
Practical Management Science
- Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?arrow_forwardIf a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.arrow_forwardUsing the same file but with a different worksheet, solve the following problem. Rename the worksheet as Problem 2. Submit the same file that shows the solution (tables with optimal answers). Dr. S, the Dean of RVR COB, has decided to apply a new method in assigning professors to courses next trimester. As a criterion for judging who should teach each course, Dean S reviews the past two years' teaching evaluations. Since each of the four professors taught each of the four courses at one time or another during the two-year period, Dr. S can record a course rating for each instructor. Find the best assignment for professors. PROFESSOR STATISTICS ACCOUNTING FINANCE ECONOMICS Andy Benny Charles Dennis 90 70 85 55 Course Upload Choose a File 65 60 40 80 95 80 80 65 40 75 60 55 Which professor should be assigned to teach each of those courses?arrow_forward
- An analyst has started preparing a spreadsheet as shown below. Column A contains the headings for various parameters and Column B contains the analyst's range names to be used in Excel. A B 1 Price per Unit 2 Cost per Unit 3 Profit per Unit PricePerUnit Cost_Per_Unit Profit per Unit 4 5 Fixed Costs Fixed_Costs 6 Variable Costs Variable Costs Label each of the following range names as "Correct" if is a valid range name in Excel or "Incorrect" if the range name is not valid for use in Excel. Proposed Range Name PricePerUnit Cost Per_Unit Profit per Unit Fixed_Costs Variable Costsarrow_forwardASK YOUR TEACHER PRACTICE ANOTHER A linear programming computer package is needed. Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company's needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows. Supplier Component 1 2 3 1 $11 $12 $13 2 $9 $10 $9 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows. Supplier 1 2 3 Capacity 400 800 600 (a) If the Edwards production plan for the next period includes 800 units of component 1 and 600 units of component 2, what purchases do you recommend?…arrow_forwardA linear programming computer package is needed. Hilltop Coffee manufactures a coffee product by blending three types of coffee beans. The cost per pound and the available pounds of each bean are as follows. Bean Cost per Pound Available Pounds 1 2 3 1 $0.50 2 $0.70 3 $0.45 Consumer tests with coffee products were used to provide ratings on a scale of 0-100, with higher ratings indicating higher quality. Product quality standards for the blended coffee require a consumer rating for aroma to be at least 75 and a consumer rating for taste to be at least 80. The individual ratings of the aroma and taste for coffee made from 100% of each bean are as follows: Bean Aroma Rating Taste Rating 75 85 60 85 lb lb lb 450 87 650 74 450 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 blend. (a) What is the minimum-cost blend (in pounds) that will meet the quality standards and provide 1,000 pounds of the blended…arrow_forward
- Company aims to determine the optimal number of products to be produced in order to maximize the total profit. a) Formulate the problem using algebraic method. b) Solve the model using the graphical method (indicate optimal solution and profit). C) again). Use graphical method to determine the shadow price for each of these resources (based on the definition of shadow price and by increasing each resource by one unit and solving the problem d) Use the Excel solver to do parts b and c. e) follow: Using Solver Table generate the optimal solution and the total profit for each resource as e1: Consider unit profit for product 1 (use range from 0 to 4 and increment of 1) e2: Consider unit profit for product 2 (use range from 0 to 4 and increment of 1) е3: Consider simultaneous changes for both unit profits in part e1 and e2 using given ranges. e4: Consider available resource of Raw material 1 (use range from 2 to 14 and increment of 1) e5: Consider available resource of Raw material 2 (use…arrow_forwardHi... I'm having trouble with the following: Min Jee wants to combine the sales data from each of the art fairs. Switch to the Combined Sales worksheet, and then update the worksheet as follows: In cell A5, enter a formula without using a function that references cell A5 in the Madison Copy the formula from cell A5 to the range A6:A8 without copying the formatting. In cell B5, enter a formula using the SUM function, 3-D references, and grouped worksheets that totals the values from cell B5 in the Chicago:Madison Copy the formula from cell B5 to the range B6:B8 without copying the formatting. Copy the formulas and the formatting from the range B5:B8 to the range C5:E8. (Hint: You can ignore the error about empty cells because Min Jee will enter the Madison sales data later.)arrow_forwardRefer to the Factory-to-Six-Customers problem and start with the original information. Each customer increases demand by 1000 units. This increased demand has to be met. Re-calculate the optimal solution. At the new solution, which of the following statements is true? A. The total shipping costs are $252,900 B. Quantity shipped from Factory 1 to Customer 1 declines by 6000 units C. Both A and B D. Neither A norarrow_forward
- Pls help ASAP for botharrow_forwardPlease do not give solution in image format thankuarrow_forwardContois Carpets is a small manufacturer of carpeting for home and office installations. Production capacity, demand, production cost per square yard (in dollars), and inventory holding cost per square yard (in dollars) for the next four quarters are shown in the network diagram below. Min s.t. Beginning Inventory Flow x26 Quarter 1 Demand Flow X37 X48 50 Quarter 1 Production Flow Quarter 2 Demand Flow X59 600 Quarter 2 Production Flow Quarter 3 Demand Flow X67 300 Quarter 3 Production Flow Quarter 4 Demand Flow X78 500 Quarter 4 Production Flow X89 X910 400 = $ Production Capacities Develop a linear programming model to minimize cost and meet demand exactly. (Let Xij which flows from node i to node j.) = $ = $ = $ = $ Ending Inventory Flow ≥ 0 for all i, j. Solve the linear program to find the optimal solution. X16 = $ = $ Production Nodes = $ = $ 2 Quarter 1 Production 3 Quarter 2 Production 4 Quarter 3 Production 1 Beginning Inventory 5 Quarter 4 Production Production Cost Per Square…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,