Techno Corporation is currently manufacturing an item at variable costs of $$4$ per unit. Annual fixed costs of manufacturing this item are $$142,000.$ The current selling price of the item is $$11$ per unit, and the annual sales volume is $30,000$ units.

a$.$ Techno can substantially improve the item's quality by installing new equipment at additional annual fixed costs of $$60,000.$ Variable costs per unit would increase by $$2,$ but, as more of the better$-$quality product could be sold, the annual volume would increase to $55,000$ units. Should Techno buy the new equipment and maintain the current price of the item? Why or why not?

Yes, because the profit increases from $$68000$ to $$73000.($Enter your responses as integers.$)$

b$.$ Alternatively, Techno could increase the selling price to $$12$ per unit. However, the annual sales volume would be limited to $40,000$ units. Should Techno buy the new equipment and raise the price of the item? Why or why not?