Problem $2$

The labor cost to produce a widget is $$10\mathrm{.}50$ per hour. A one$-$time job setup cost of $$50$ and material costs are $$20$ per unit. The overhead cost is charged as $50\%$ of the labor, materials, and setup costs. The learning rate is $90\%.$

a$.$ Determine the average cost for $20$ units, given that the first unit took $5$ hours to complete.

b$.$ Assume the item can be purchased from a vendor for $$88\mathrm{.}50$ per unit. Should we just buy the needed $20$ units or produce them. Explain.

c$.$ What are your answers for a and $b$ if the needed quantity is $40$ units? Show all your work.