Alpha and Beta are divisions within the same company. The managers of both divisions are evaluated based on their own divisions 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 $$2$ per unit in commissions on any sales to Beta Division.a$.$ What is Alpha Division's lowest acceptable transfer price?b$.$ What is Beta Division's highest acceptable transfer price?c$.$ What is the range of acceptable transfer prices $($if any$)$ between the two divisions? Will the managers probably agree to a transfer?$2.$ Refer to case $2$ shown above. A study indicates that Alpha Division can avoid $$5$ per unit in shipping costs on any sales to Beta Division.a$.$ What is Alpha Division's lowest acceptable transfer price?b$.$ What is Beta Division's highest acceptable transfer price?c$.$ What is the range of acceptable transfer prices $($if any$)$ between the two divisions? Would you expect any disagreement between the two divisional managers over what the exact transfer price should be$?$d$.$ Assume Alpha Division offers to sell $30,000$ units to Beta Division for $$88$ per unit and that Beta Division refuses this price. What will be the loss in potential profits for the company as a whole?$3.$ Refer to case $3$ shown above. Assume that Beta Division is now receiving an $8\%$ price discount from the outside supplier.a$.$ What is Alpha Division's lowest acceptable transfer price?b$.$ What is Beta Division's highest acceptable transfer price?c$.$ What is the range of acceptable transfer prices $($if any$)$ between the two divisions? Will the managers probably agree to a transfer?d$.$ Assume Beta Division offers to purchase $20,000$ units from Alpha Division at $$60$ per unit. If Alpha Division accepts this price, would you expect its ROI to increase, decrease, or remain unchanged?$4.$ Refer to case $4$ shown above. Assume that Beta Division wants Alpha Division to provide it with $120,000$ units of a different product from the one Alpha Division is producing now. The new product would require $$21$ per unit in variable costs and would require that Alpha Division cut back production of its present product by $45,000$ units annually. What is Alpha Divisions lowest acceptable transfer price