Division A$\text{'}$s cost accounting records show that the cost of its product is $$154$ per unit$-$ $$109$ in variable costs and $$45$ in fixed costs. The market price of the product, $$163,$ barely covers Division A$\text{'}$s cost of production plus its selling and administrative costs. Division A has a maximum capacity of $109,600$ units; it is currently producing and selling $80,000$ units. Division B makes a product that uses Division A$\text{'}$s product and would like to purchase $12,200$ units from Division A for $$152.$ With $$45$ additional variable costs, Division B produces and sells the product for $$230.$ Division A$\text{'}$s manager is not happy with Division B$\text{'}$s offer and is refusing to sell.

Calculate the increase in corporate income in the following situations:

a$.$ Division A sells $12,200$ units to Division B for $$152$ each, and Division B produces and sells $12,200$ units for $$230.$

b$.$ Division A does not sell to Division B$.$ Division B purchases $12,200$ units from an external supplier at $$163$ each and produces and sells $12,200$ units for $$230.$