@article{MAKHILLJEAS2019141718297,
    title = {A Quantum Calculus Analogue of Dynamic Leontief Production Model with
Quadratic Objective Function},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {14},
    number = {17},
    pages = {6415-6418},
    year = {2019},
    issn = {1816-949x},
    doi = {jeasci.2019.6415.6418},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2019.6415.6418},
    author = {Rasheed,Ali and},
    keywords = {Leontief production model,quantum calculus,quadratic objective function,primal model,dual
model,duality theorems},
    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.}
    }