5. A company is considering an expansion into five new sales territories. The company has four salesmen.Based on the salesmen's experiences and capability the TSM has estimated required time (days) for eachof the salesmen to complete the advertising campaign in each of the sales territories. The estimateddurations are as follows:TERRITORIES134s17580857090SALESS29171827585MENS37890858080S46575888590Suggest optimum assignment of the salesmen. If for certain reasons, salesman S4 cannot be assigned toterritory 3, will the optimum assignment be different? If so, what would be the new assignment schedule?

The question is unbalanced problem of minimization. In order to balance it we will insert a dummy…

Answered: 5. A company is considering an…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 59P

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1. A city is reviewing the location of its fire stations. The city is made up of a number of neighborhoods, as illustrated in the figure below. A fire station can be placed in any neighborhood. It is able to handle the fires for both its neighborhood and any adjacent neighborhood (any neighborhood with a non-zero border with its home neighborhood). The objective is to minimize the number of fire stations used. Solve this problem. Which neighborhoods will be hosting the firestations?
57. A beer company has divided Bloomington intotwo territories. If the company spends x1 dollarson promotion in territory 1, it can sell 60x11y2 casesof beer there; and if it spends x2 dollars on promotion in territory 2, it can sell 40x21y2 cases of beerthere. Each case of beer sold in territory 1 sells for$10 and incurs $5 in shipping and production costs.Each case of beer sold in territory 2 sells for $9 andincurs $4 in shipping and production costs. A total of$5000 is available for promotion.a. How can the company maximize its profit?b. If an extra dollar could be spent on promotion, byapproximately how much would the company’sprofit increase? By how much would its revenueincrease?c. Use SolverTable to see how a change in the priceof beer 1 affects the optimal solution. Do the samefor a change in the price of beer 2.
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Problem There are three factories on the Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton. It costs $1000 to process a ton of factory 2 waste, and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton. It costs $2000 to process a ton of factory 3 waste, and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.30 ton. The state wants to reduce the amount of P 1in the river by at least 30 tons and the amount of P2 by at least 40 tons. Use Solver to determine how to minimize the cost of reducing pollution by the desired amounts. Use SolverTable to investigate the effects of increases in the minimal reductions required by the state. Specifically, see what…
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The government is auctioning off oil leases at two sites. At each site, 150,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bid- ding for the oil. Government rules state that no bidder can receive more than 45% of the land being auctioned. Cliff has bid $2000 per acre for site 1 land and $1000 per acre for site 2 land. Blake has bid $1800 per acre for site 1 land and $1500 per acre for site 2 land. Alexis has bid $1900 per acre for site 1 land and $1300 per acre for site 2 land. Determine how to maximize the government’s revenue with a transportation model.Use SolverTable to see how changes in the government’s rule on 45% of all land being auctioned affect the optimal revenue. Why can the optimal revenue not decrease if this percentage required increases? Why can the optimal revenue not increase if this percentage required decreases?
The Janie Gioffre Drapery Company makes three types of draperies at two different locations. At location I, it can make 10 pairs of deluxe drapes, 20 pairs of better drapes, and 13 pairs of standard drapes per day. At location II, it can make 20 pairs of deluxe, 50 pairs of better, and 6 pairs of standard per day. The company has orders for 3000 pairs of deluxe drapes, 6300 pairs of better drapes, and 1800 pairs of standard drapes. If the daily costs are $750 per day at location I and $900 per day at location II, how many days should Janie schedule at each location to fill the orders at minimum cost? location I days location II days Find the minimum cost.$
Consider the following puzzle. You are to pick out 4three-letter “words” from the following list:DBA DEG ADI FFD GHI BCD FDF BAIFor each word, you earn a score equal to the position thatthe word’s third letter appears in the alphabet. For example,DBA earns a score of 1, DEG earns a score of 7, and so on.Your goal is to choose the four words that maximize yourtotal score, subject to the following constraint: The sum ofthe positions in the alphabet for the first letter of each wordchosen must be at least as large as the sum of the positionsin the alphabet for the second letter of each word chosen.Formulate an IP to solve this problem.
The government is auctioning off oil leases at two sites. At each site, 150,000 acres of land are to be auctioned. Cliff Ewing, Blake Barnes, and Alexis Pickens are bidding for the oil. Government rules state that no bidder can receive more than 45% of the land being auctioned. Cliff has bid $2000 per acre for site 1 land and $1000 per acre for site 2 land. Blake has bid $1800 per acre for site 1 land and $1500 per acre for site 2 land.Alexis has bid $1900 per acre for site 1 land and $1300 per acre for site 2 land.a. Determine how to maximize the government’s revenue with a transportation model.b. Use SolverTable to see how changes in the government’s rule on 45% of all land being auctioned affect the optimal revenue. Why can theoptimal revenue not decrease if this percentage required increases? Why can the optimal revenue not increase if this percentage required decreases?

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