Given that department M's indirect costs total $825,000 and it expects to use 50,000 machine hours to allocate these costs using machine hours as the cost driver. We are to determine the cost per machine hour so that we can determine the cost of inventory. The cost per machine hour can be determined using the following formula:Cost per machine hour = Indirect costs / Machine hoursSubstituting the values given, we get;Cost per machine hour = $825,000 / 50,000 mCost per machine hour = $16.50/machine hourTherefore, the cost of inventory for a product that takes 500 machine hours in department M is:Cost of inventory = Number of machine hours x Cost per machine hour= 500 m x $16.50/m = $8,250.Hence, the cost of inventory for a product that takes 500 machine hours in department M is $8,250.