The fast-paced evolution of digital retail requires the enhanced application of quantitative analysis of decisions related to pricing, demand forecasting, inventory control and fulfillment. In this paper, there is a mathematical treatment of the modern business model of quick commerce and how the tools of calculus and business mathematics can be employed in order to analyze the decisions related to it.  For this purpose, a linear inverse demand function is constructed that sets the connection between price and quantity. Using this connection, a quadratic function of revenue is developed and then marginal revenue is found out via differentiation.  Further, a nonlinear cost function that reflects the fixed operating cost, variable costs and increasing marginal cost is constructed.  Using the profit function, its first derivative is found in order to find out the stationary level of output and the second derivative helps in defining the characteristics of this point. Moreover, price elasticity is computed in order to measure the degree of sensitivity of demand to the price change. The numerical values are fictional and are used for the purpose of demonstrating the process of mathematical analysis. The study is contextualized within the context of digital commerce within India, which entails the emergence of quick commerce and an open digital commerce infrastructure like ONDC. Calculus will serve as a tool for developing an interpretable and coherent relationship between mathematical theory and the practical aspects of commerce.