Walker Limited wants to incorporate the effects of learning into the cost of producing a component used in the laser printers it sells to commercial print shops. The standard cost of direct materials for the component is $$40$ per unit. Budgeted setup costs are $$100$ per setup. The standard rate for direct labour is $$20$ per hour, and the standard variable overhead rate is $150\%$ of direct labour costs. Production of the component is a repetitive process that requires experience to reach maximum productivity levels. Standards reflect a $70\%$ learning rate. The initial component requires $10$ hours to produce.

$1.$ Determine the average unit cost of eight units using the cumulative average time approach.

$2.$ If the component can be purchased from an external supplier for $$310$ per unit, at what level of production would Walker Limited be indifferent between producing the component internally and buying it from the supplier?