Abstract: In this study, we derive a new formulation for the dynamic Leontief production model with quadratic objective function using quantum calculus analogue. Our new formulation unifies discrete and continuous Leontief production models. Also, the classical Leontief production model is obtained by choosing q = 1. In addition, we give an introduction to quantum calculus. We formulate the primal and the dual continuous Leontief production models with quadratic objective function as well as quantum calculus models. Furthermore, we can get upper and lower bounds for the value of production at any production plan using the quadratic objective functions for the primal and the dual quantum calculus models. Moreover, the duality theorem for quantum calculus analogue are established. Finally, example is given in order to show the new results.