Concept explainers
(a)
Interpretation: For the situation described in Problem 28, the gravity solution needs to be determined.
Concept Introduction: In a gravity problem, the objective becomes appropriate when the cost for locating new facilities goes up, as the function of square of distances between the new facility to the existing facility.
(b)
Interpretation: For the situation described in Problem 28, by using the answer obtained in part (a) as an initial solution for the Euclidean distance problem, and if it is solved by hand then
Concept Introduction: In a Euclidean space, the distance between two points, in a straight line is called Euclidean distance.
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EBK PRODUCTION AND OPERATIONS ANALYSIS
- 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_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_forwardCan you solve it mathematically using an equation?arrow_forward
- A company manufactures a product at its plants in A, B, and C, then ships the product to six customers in G, H, J, K, and L. The monthly capacity of plants A, B, and Care 7300, 7400, and 7500 units, respectively. The monthly demand from customers G, H, J, K, and Lare. 1200, 8900, 7600, 2600, and 1500 units, respectively. Use Excel Solver to find the optimal distribution plant that will give the lowest total monthly shipping cost if the shipping cost per unit (in dollars per unit) are as follows: from A to G, H, J, K, and L are 4, 9, 20, 6, and 13 dollars per unit, respectively; from B to G, H, J, K, and Lare 7, 6, 12, 2, and 9 dollars per unit, respectively; from C to G, H, J, K, and Lare 12, 7, 3, 17, and 6 dollars per unit, respectively. The optimal total shipping costs is dollars per montharrow_forwardMultiple Optimal Solution: Example (9): Find the optimal solution for the : Multiple Optimal following model by the graphical method Max Z = X,+X, X, +X, 23 .(1) X, +X, 56 S. to : X,21 ..(2) .(3) X, s2 (4) X, 20 X, 20arrow_forwardFor the following problem, provide an objective in words, data definition, variable definition, and algebraic formulation (using summation notation when possible). You do not need to implement and solve. Submit your solution as an attached file. You may type up your work using Microsoft Word. Hire-a-Car System rents three types of cars at two different locations. The profit contribution made per day for each car type at each location is listed below. Car Type Location Economy Mid-size Luxury A $25 $40 $10 $30 $35 $45 The management forecasts the demand per day by car type as follows: 125 rentals for Economy cars, 55 rentals for Mid-size cars, and 40 rentals for Luxury cars. The vehicle capacity of each location is 100 cars in location A and 120 cars in location B.arrow_forward
- i need the solution for this question using excel solver ( simplex method ) send me a screenshot of the solution in excelarrow_forwardLong-Life Insurance has developed a linear model that it uses to determine the amount of term life Insurance a family of four should have, based on the current age of the head of the household. The equation is: y=150 -0.10x where y= Insurance needed ($000) x = Current age of head of household b. Use the equation to determine the amount of term life Insurance to recommend for a family of four of the head of the household is 40 years old. (Round your answer to 2 decimal places.) Amount of term life insurance thousandsarrow_forwardLong-Life Insurance has developed a linear model that it uses to determine the amount of term life insurance a family of four should have, based on the current age of the head of the household. The equation is:y = 850 − .1xwherey = Insurance needed ($000)x = Current age of head of household a. Plot the relationship on a graph. b. Use the equation to determine the amount of term life insurance to recommend for a family of four if the head of the household is 30 years old.arrow_forward
- Ohio Swiss Milk Products manufactures and distributes ice cream in Ohio, Kentucky, and West Virginia. The company wants to expand operations by locating another plant in northern Ohio. The size of the new plant will be a function of the expected demand for ice cream within the area served by the plant. A market survey is currently under way to determine that demand. Ohio Swiss wants to estimate the relationship between the manufacturing cost per gallon and the number of gallons sold in a year to determine the demand for ice cream and, thus, the size of the new plant. The following data have been collected: ITT Cost per Thousand Gallons (Y) $1,024 Thousands of Gallons Sold (X) 434.7 Plant 962 466.4 251.3 372. 1,065 1,006 1.045 245.0 258.6 1,068 988 997 1,063 1,000 $10.218 614.9 414.0 267.5 380,4 3 704 9 9 10 Total a. Develop a regression equation to forecast the cost per thousand gallons as a function of the number of thousands of gallons produced. The forecasting model is given by the…arrow_forwardOhio Swiss Milk Products manufactures and distributes ice cream in Ohio, Kentucky, and West Virginia. The company wants to expand operations by locating another plant in northern Ohio. The size of the new plant will be a function of the expected demand for ice cream within the area served by the plant. A market survey is currently under way to determine that demand. Ohio Swiss wants to estimate the relationship between the manufacturing cost per gallon and the number of gallons sold in a year to determine the demand for ice cream and, thus, the size of the new plant. The following data have been collected: ITT Plant 1 Cost per Thousand Gallons (Y) $1,024 Thousands of Gallons Sold (X) 434.7 2 962 466.4 3 1,065 1,006 1,045 1,068 251.3 372.1 5 245.0 258.6 614.9 7 988 8. 997 414.0 267.5 380.4 3,704.9 9 1,063 1,000 $10,218 10 Total a. Develop a regression equation to forecast the cost per thousand gallons as a function of the number of thousands of gallons produced. The forecasting model is…arrow_forwardOhio Swiss Milk Products manufactures and distributes ice cream in Ohio, Kentucky, and West Virginia. The company wants to expand operations by locating another plant in northern Ohio. The size of the new plant will be a function of the expected demand for ice cream within the area served by the plant. A market survey is currently under way to determine that demand. Ohio Swiss wants to estimate the relationship between the manufacturing cost per gallon and the number of gallons sold in a year to determine the demand for ice cream and, thus, the size of the new plant. The following data have been collected: Plant ITT Thousands of Gallons Sold (X) 434.7 Cost per Thousand Gallons (Y) 1 $1,024 2 962 466.4 3 1,065 1,006 1,045 1,068 251.3 372.1 5 245.0 6. 258.6 7 988 614.9 414.0 8 997 9 1,063 1,000 $10,218 267.5 380,4 3,704.9 10 Total a. Develop a regression equation to forecast the cost per thousand gallons as a function of the number of thousands of gallons produced. The forecasting model…arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,