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3.4-9. Web Mercantile sells many household products through an on-line catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing ware- house storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most eco- nomical to lease only the amount needed each month on a month- by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month. The space requirement and the leasing costs for the various leasing periods are as follows: Required Month Space (Sq. Ft.) Leasing Period Cost per Sq. Ft. (Months) Leased $ 65 $100 30,000 20,000 40,000 10,000 50,000 1 1 3 $135 4 4 $160 5 $190 The objective is to minimize the total leasing cost for meeting the space requirements. (a) Formulate a linear programming model for this problem. c (b) Solve this model by the simplex method.

3.4-9. Web Mercantile sells many household products through an on-line catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing ware- house storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most eco- nomical to lease only the amount needed each month on a month- by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month. The space requirement and the leasing costs for the various leasing periods are as follows: Required Month Space (Sq. Ft.) Leasing Period Cost per Sq. Ft. (Months) Leased $ 65 $100 30,000 20,000 40,000 10,000 50,000 1 1 3 $135 4 4 $160 5 $190 The objective is to minimize the total leasing cost for meeting the space requirements. (a) Formulate a linear programming model for this problem. c (b) Solve this model by the simplex method.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.5: Shortest Path Models
Problem 34P
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3.4-9. Web Mercantile sells many household products through an on-line catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing ware- house storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most eco- nomical to lease only the amount needed each month on a month- by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month. The space requirement and the leasing costs for the various leasing periods are as follows: Required Month Space (Sq. Ft.) Leasing Period Cost per Sq. Ft. (Months) Leased $ 65 30,000 20,000 40,000 10,000 50,000 1 1 2 $100 3 3 $135 4 4 $160 $190 The objective is to minimize the total leasing cost for meeting the space requirements. (a) Formulate a linear programming model for this problem. c (b) Solve this model by the simplex method. 3.4-10. Larry Edison is the director of the Computer Center for
Transcribed Image Text:3.4-9. Web Mercantile sells many household products through an on-line catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing ware- house storage space over the next 5 months. Just how much space will be required in each of these months is known. However, since these space requirements are quite different, it may be most eco- nomical to lease only the amount needed each month on a month- by-month basis. On the other hand, the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased (by adding a new lease and/or having an old lease expire) at least once but not every month. The space requirement and the leasing costs for the various leasing periods are as follows: Required Month Space (Sq. Ft.) Leasing Period Cost per Sq. Ft. (Months) Leased $ 65 30,000 20,000 40,000 10,000 50,000 1 1 2 $100 3 3 $135 4 4 $160 $190 The objective is to minimize the total leasing cost for meeting the space requirements. (a) Formulate a linear programming model for this problem. c (b) Solve this model by the simplex method. 3.4-10. Larry Edison is the director of the Computer Center for
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