The work described in this paper models the scheduling of smart home appliances of different types of consumers based on their sensitivity to dynamic price changes. The price sensitivity is established on a scale of 0 to 100 percent. We have used Linear programming to optimally schedule a set of residential appliances under variable peak pricing in order to minimize the consumer’s energy bill. This paper shows different scheduling models for the home appliances for different categories of price sensitive consumers. It takes into consideration that all consumers have access to perfect information such that they can alter their usage and thereby benefit from the associated cost savings. We also analyze the monthly electricity cost/expenditure against price sensitivity and define a function for the same.