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Problem statement: We studied the inventory-production system with two-parameter Weibull distributed deterioration items. Approach: The inventory model was developed as linear optimal control problem and by the Pontryagin maximum principle, the optimal control problem was solved analytically to obtain the optimal solution of the problem. Results: It was then illustrated with the help of an example. By the principle of optimality we also established the Riccati based solution of thedoi:10.3844/jmssp.2009.206.214 fatcat:pvqv5fwr2fchblltgwopjccq3m