Alpha and Beta are divisions within the same company. The managers of both divisions are evaluated based on their own division$$s return on investment $($ROI$).$ Assume the following information relative to the two divisions:

Case

$1234$

Alpha Division:

Capacity in units $80,000400,000150,000300,000$

Number of units now being sold to outside customers $80,000400,000100,000300,000$

Selling price per unit to outside customers $ $30$ $ $90$ $ $75$ $ $50$

Variable costs per unit $ $18$ $ $65$ $ $40$ $ $26$

Fixed costs per unit $($based on capacity$)$ $ $6$ $ $15$ $ $20$ $ $9$

Beta Division:

Number of units needed annually $5,00030,00020,000120,000$

Purchase price now being paid to an outside supplier $ $27$ $ $89$ $ $75*$

$*$Before any purchase discount.

Required:

$1.$ Refer to case $1$ shown above. Alpha Division can avoid $$2$ per unit in commissions on any sales to Beta Division.

a$.$ What is Alpha Division's lowest acceptable transfer price?

$2)$

d$.$ Assume Alpha Division offers to sell $30,000$ units to Beta Division for $$88$ per unit and that Beta Division refuses this price. What will be the loss in potential profits for the company as a whole?