$3.(10$ points$).$ Safsufa Inc. has two divisions: Alpha and Beta. The Alpha Division manufactures product A$1$ and has a production capacity of $80,000$ units, with machine hours being the constrained resource. The Alpha Division currently sells $70,000$ units of product A$1.$ The Beta Division would like to manufacture Product B$2,$ which requires a component called B$1.$ There is no outside market for component B$1,$ however, the Alpha Division has the capability to manufacture component B$1.$ At the Alpha Division, product A$1$ requires $6$ minutes of machine time, and component B$1$ would require $18$ minutes of machine time, and the variable costs per unit of B$1$ are $\backslash (\backslash$$ $50\backslash ).$ The following table provides additional relevant production cost information for both divisions: At the Beta Division, the $\backslash (\backslash$$ $60\backslash )$ variable costs per unit of Product B$2$ in the table above, are in addition to cost of the transfer price of component B$1.$ The Beta Division manager approached the Alpha Division manager with a request for $10,000$ units of component B$1.$ The B$1$ order is all or nothing. Assume the Beta Division does not have an alternative use for it production capacity of product B$2.$ a$.$ What is the minimum transfer price per unit for component B$1$ acceptable to the Alpha Division manager? b$.$ What is the maximum transfer price acceptable to the Beta Division manager?