Johnson Inc. produces two products, X and Y from a single joint process, costing $$10,000,$ which is allocated evenly to each product. Johnson Inc. will produce $10,000$ units of each product. Product X can be sold in its current format for $$20$ per unit. Product X incurs $$12$ of variable costs per unit. Product Y can be sold in its current format for $$25$ per unit. Product Y incurs $$12$ of variable costs per unit.

Alternatively, Products X and Y can be processed further and then resold. Product X can be processed further into $8,000$ units of Product X$1.$ Product Y can be further processed into $10,000$ units Product Y$1.$

$-$ Product X$1$ would sell for $$30$ per unit and cost a total of $$30,000.$

$-$ Product Y$1$ would sell for $$35$ per unit and cost a total of $$120,000.$

Based on the information provided, what is the optimal production plan for Johnson Inc?

Select one:

a$.$ Product X and Product Y$1.$

b$.$ Product X and Product Y$.$

c$.$ Product X$1$ and Product Y$.$

d$.$ Product X$1$ and Product Y$1.$