Help with If and sum and Vlookup formula

Hi All

I have attached a sample file. I need assistance with a complex formula to achieve a required result. Please have a look and see if it can be done.
1.My workbook consists of 3 sheets. Hist, Ingredients & Prep.
2. Hist contains the Qty sales of a specific menu item.
3. Ingredients contains the breakdown of the stock involved for that specific menu item.
4. Prep contains a stock take of the individual items relating to the sale of the specific menu item.
5. Prep has a area highlighted in yellow with the required result......This is where the formula needs to be.
6. The values are as follows:

6.1. Sirloin 3 as there is 1 with the (1)Chef Steak and 2 with the (2)Surfer Steaks sold
6.2. Beef Pattie 1 as there is 1 with the (1)Burger sold
6.3. Rolls 8 as there is 1 with the (1)Burger, 4 with the (2)Full Breakfast Buns and 3 with the (3)Half Breakfast Buns
6.4. Bacon Portions are 7 as there are 4 with the (2)Full Breakfast Buns and 3 with the (3)Half Breakfast Buns
6.5. Chip portions are 4 as there is 1 with the (1)Burger and 1 with the 1()Chef's Steak and 2 with the (2)Surfer Steaks.
6.6. Eggs are 7 as there is 4 with the (2)Full Breakfast Buns and 3 with the (3)Half Breakfast Buns

Is there a formula that can be used in all the cells to produce this result?