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1. The Energetic company needs to make plans for the energy systems for a new building. The energy needs in the building fall into three categories: (1) electricity, (2) heating water, and (3) heating space in the building. The daily requirements for these three categories (all measured in the same units) are 20 electricity units, 10 heating water units, and 30 space heating units. The three possible sources of energy to meet these needs are electricity, natural gas, and a solar heating unit that can be installed on the roof. The size of the roof limits the largest possible solar heater to 30 units, but there is no limit to the electricity and natural gas available. Electricity needs can be met only by purchasing electricity (at a cost of 50 KWD per unit). Both other energy needs can be met by any source or combination of sources. The unit costs are given in the following table. Electricity Natural Gas Solar Heater

1. The Energetic company needs to make plans for the energy systems for a new building. The energy needs in the building fall into three categories: (1) electricity, (2) heating water, and (3) heating space in the building. The daily requirements for these three categories (all measured in the same units) are 20 electricity units, 10 heating water units, and 30 space heating units. The three possible sources of energy to meet these needs are electricity, natural gas, and a solar heating unit that can be installed on the roof. The size of the roof limits the largest possible solar heater to 30 units, but there is no limit to the electricity and natural gas available. Electricity needs can be met only by purchasing electricity (at a cost of 50 KWD per unit). Both other energy needs can be met by any source or combination of sources. The unit costs are given in the following table. Electricity Natural Gas Solar Heater

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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1. The Energetic company needs to make plans for the energy systems for a new building. The energy needs in the building fall into three categories: (1) electricity, (2) heating water, and (3) heating space in the building. The daily requirements for these three categories (all measured in the same units) are 20 electricity units, 10 heating water units, and 30 space heating units. The three possible sources of energy to meet these needs are electricity, natural gas, and a solar heating unit that can be installed on the roof. The size of the roof limits the largest possible solar heater to 30 units, but there is no limit to the electricity and natural gas available. Electricity needs can be met only by purchasing electricity (at a cost of 50 KWD per unit). Both other energy needs can be met by any source or combination of sources. The unit costs are given in the following table. Water heating Space heating Electricity 90 KWD 80 KWD Natural Gas 60 KWD 50 KWD Solar Heater 30 KWD 40 KWD The objective is to minimize the total cost of meeting the energy needs. a. Define the decision variables. b. Formulate and solve a linear program to minimize the energy costs of meeting the energy needs. c. Which heating requirement (water or space) would you consider reducing to lower cost? Explain.
Transcribed Image Text:1. The Energetic company needs to make plans for the energy systems for a new building. The energy needs in the building fall into three categories: (1) electricity, (2) heating water, and (3) heating space in the building. The daily requirements for these three categories (all measured in the same units) are 20 electricity units, 10 heating water units, and 30 space heating units. The three possible sources of energy to meet these needs are electricity, natural gas, and a solar heating unit that can be installed on the roof. The size of the roof limits the largest possible solar heater to 30 units, but there is no limit to the electricity and natural gas available. Electricity needs can be met only by purchasing electricity (at a cost of 50 KWD per unit). Both other energy needs can be met by any source or combination of sources. The unit costs are given in the following table. Water heating Space heating Electricity 90 KWD 80 KWD Natural Gas 60 KWD 50 KWD Solar Heater 30 KWD 40 KWD The objective is to minimize the total cost of meeting the energy needs. a. Define the decision variables. b. Formulate and solve a linear program to minimize the energy costs of meeting the energy needs. c. Which heating requirement (water or space) would you consider reducing to lower cost? Explain.
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