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_forwardAn 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_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_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
- Please solve using Excel @Risk add-in the question is Textbook Problem from Practical Management Science 6th Edition Chapter 11.4 Problem 30P. In the solution please provided step-by-step excel formulas used. The full Question is attached in the image. Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the company’s 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. Thefollowing 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…arrow_forwardPlease answer it immediately sir Linear Programming The Booboo sawmill in Batangas produces pine and oak boards for manufacturing firms. Each month the sawmill must deliver atleast 5 tons of wood to the manufacturer . It takes the sawmill 3 days to produce a ton of pine and a 2 days to produce a ton of oak and the sawmill can allocate 18 days out of a month for this contract. The sawmill can get enough pine to make atleast 4 tons of wood and enough oak to make atmost 7 tons of wood. Determine the number of tons of pine and oak in order to minimize cost, given that pine has a cost of $3 and oak $6 to producearrow_forwardHudson Corporation is considering three options for managing its data warehouse: continuing with its own staff, hiring an outside vendor to do the managing (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The cost of the operation depends on future demand. The annual cost of each option (in thousands of dollars) depends on demand as follows: DemandStaffing Options High Medium LowOwn staff 650 650 600Outside vendor 900 600 300Combination 800 650 500(a) If the demand probabilities are 0.2, 0.5, and 0.3, which decision alternative will minimize the expected cost of the data warehouse? Outside vendorWhat is the expected annual cost associated with that recommendation? Enter your answer in thousands dollars. For example, an answer of $200 thousands should be entered as 200,000. Expected annual cost = $570000(b) Construct a risk profile for the optimal decision in part (a). The input in the box below will…arrow_forward
- A 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 $0.70 2 $0.45 3 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 85 450 87 550 74 350 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 coffee…arrow_forwardfertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1 (W1) has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows: W 1 W 2 W 3 Customer A $7.50 $6.25 $6.50 Customer B $6.75 $7.00 $8.00 Write the objective function and the constraint in equations. Let Vij= tons shipped to customer i from warehouse j, and so on. For example, VA1=tons shipped to customer A from warehouse W1. This exercise contains only parts b, c, d, e, and f. Part 2 b) The objective function for the LP model =arrow_forward1. Construct a 2-by2 contingency table to determine the total number of people who fail the screening test and will be referred for diagnostic testing in the hearing centers. 2. Construct a 2-by-2 contingency table to determine the total number of people who fail the diagnostic test, which represents the target market for hearing aid sales.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,