First I have to let out a big sigh
that they're making you learn perpetual and periodic at the same time. That's just not nice.
Here is what I got.
A) Perpetual Inventory System
Jan 2. Cash (not sure if this is what I should title the account) Debit 117,000
Sales (credit) 117,000
Jan. 5 inventory -debit 50,000
Account payable (Lunar Optics) credit 50,000
Jan. 2 cost of goods Sold - debit 90000
Inventory - Credit 90000
SHOULD I BE MAKING AN ADDITION ENTRY FOR SALES REVENUE FOR JAN 2?
Yes, it's cash. It was sold for cash, so you got cash. Unlike a lot of things in accounting, take cash literally. Yes, the second entry should be there, but get it in order with the other Jan 2 entry. In perpetual you're keeping the inventory always up-to-date, so every time a purchase it made, it goes in, and every time a sale is made, it comes back out. So that second entry is to take it out and update COGS while you're at it.
For B I am confused as to how I should compute the balance of Inventory?
It's the 210,000 you got in part d. Think about it. You had 250K, you bought 50K more, you sold 90K of it. How much is left? It's what you did in part, except you've got things switched around.
C) Periodic Inventory System
CASH (Again not sure if this should be the title) debit 117,000
Sales Credit 117,000
Jan. 5 Purchases Debit 50000
Accounts Payable (Lunar Optics) Credit 50000
Am I missing anything else?
Nope, it's all correct. The change is that you update inventory at the end of the period (like part d) instead of keeping it perpetually. So the purchase goes into the purchases account rather than inventory, and you don't update COGS every time. So the second entry for a sale is not done.
Inventory end of dec. 250000
Add: Purchases 50000
Cost of Goods Available for sale 300,000
Les Inventory 90000
Cost of Goods Sold 210,000
Is this how I compute the cost of goods for the first week of jan.
You've got the last two lines backwards. First consider the Jan 2 entry. You've only had one sale, so shouldn't COGS be the 90K? 90K isn't the ending inventory - it's the COGS. It's what got sold. The 210,000 you came up with here is the answer to b, which is used to do d.
D) Because Sky Probe sells telescopes for a high cost and has only made one sale transaction so far this year, I would say it is possbile they use a perpetual inventory system.
I think the answer is another method, but it's not a choice. So given the choices, I would agree with you.