Depending on the availability of parts, a company can manufacture 3, 4, 5, or 6 units of a certain item per week with corresponding probabilities of  0.10,0.40, 0.30, and 0.20. The probabilities that there will be a weekly demand for \(0,1,2,3, \ldots\), or 8 units are, respectively, \(0.05,0.10,0.30,0.30,0.10,0.05,0.05,0.04\), and 0.01. If a unit is sold during the week that it is made, it will yield a profit of \(\$ 100\); this profit is reduced by \(\$ 20\) for each week that a unit has to be stored. Simulate the operation of this company for 50 consecutive weeks and estimate its expected weekly profit.