3. 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 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. Electricity can supply up to 20 units and natural gas can supply up to 15 units . Electricity needs can be met only by purchasing electricity (at a cost of $50 per unit). Both other energy needs can be met by any source or combination of sources. The unit costs are

Practical Management Science
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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. Electricity can supply up to 20 units and natural gas can
supply up to 15 units . Electricity needs can be met only by purchasing electricity (at a cost
of $50 per unit). Both ather energy needs can be met by any source or combination of
sources. The unit cost are
Electricity
Natural Gas
Solar Heater
Water Heating
$90
$60
$30
Space Heating
$80
$50
$40
The objective is to minimize the total cost of meeting the energy needs.
(a) Formulate this problem as a transportation problem by constructing the appropriate
parameter table.
(b) Use northwest corner rule to obtain the initial solution for this problem.
(c) Starting with the initial solution, apply the stepping stone method to obtain the optimal
solution.
Transcribed Image Text: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. Electricity can supply up to 20 units and natural gas can supply up to 15 units . Electricity needs can be met only by purchasing electricity (at a cost of $50 per unit). Both ather energy needs can be met by any source or combination of sources. The unit cost are Electricity Natural Gas Solar Heater Water Heating $90 $60 $30 Space Heating $80 $50 $40 The objective is to minimize the total cost of meeting the energy needs. (a) Formulate this problem as a transportation problem by constructing the appropriate parameter table. (b) Use northwest corner rule to obtain the initial solution for this problem. (c) Starting with the initial solution, apply the stepping stone method to obtain the optimal solution.
3. 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
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. Electricity can supply up to 20 units and natural gas can
supply up to 15 units . Electricity needs can be met only by purchasing electricity (at a cost
of $50 per unit). Both other energy needs can be met by any source or combination of
sources. The unit costs are
Electricity
20 units
Water heating
10 units
Space heating
30 units
Transcribed Image Text:3. 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 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. Electricity can supply up to 20 units and natural gas can supply up to 15 units . Electricity needs can be met only by purchasing electricity (at a cost of $50 per unit). Both other energy needs can be met by any source or combination of sources. The unit costs are Electricity 20 units Water heating 10 units Space heating 30 units
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