Whether the given linear programming problem can be stated as a standard maximisation problem. Maximize p = − 3 x − 2 y Subject to x − y + z ≥ 0 x − y − z ≥ − 6 x ≥ 0 , y ≥ 0 , z ≥ 0

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A New Heating System A homeowner wants to replace their old heating system. Energy is measured in kilowatt-hours (kWh). It takes about 11,700 kWh of energy to heat the house for the winter. The current heating system uses natural gas and is 60% efficient, which means that for every 100 kWh of natural gas it uses, it produces 60 kWh of heat. With the homeowner's current system, it costs $975 to heat the house. Assume that natural gas costs $0.05/kWh and electricity costs $0.21/kWh. The homeowner also has an air conditioner that uses 2,500 kWh of electricity per year and produces 290 kWh of cooling for every 100 kWh it uses. They also have a water heater that uses 4,300 kWh of electricity per year and produces 90 kWh of heat for every 100 kWh it uses. These systems could also be replaced if there is a cheaper option, but it isn't necessary. Here are three other types of heating systems the homeowner could replace their current system with: • A new furnace which also runs on natural gas…

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Question

Chapter 6.3, Problem 48E

To determine

Whether the given linear programming problem can be stated as a standard maximisation problem.

Maximize p=−3x−2y

Subject to

x−y+z≥0x−y−z≥−6x≥0,y≥0,z≥0

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