This paper examines the allocation of resource to different tasks in a production company. The company produces the same kinds of goods and want to allocate m number of tasks to 50 number of machines. These machines are subject to breakdown. It is expected that the breakdown machines will be repaired and put into operation. From past records, the company estimated the profit the machines will generate from the various tasks at the first stage of the operation. Also, the company estimated the probability of breakdown of the machines for performing each of the tasks. The aim of this paper is to determine the expected maximize profit that will accrue to the company over T horizon. The profit that will accrued to the company was obtained as 4, N 571,100, 000 after 48 weeks of operation. At the infinty horizon, the profit was obtained to be 20, N 491, 000, 000 . It was found that adequate planning, prompt and effective maintainance can enhance the profitability of the company.