Limiting factors

Dear Mr Moffat, I did the following question which was fine until the end where I have a doubt for which I would like to ask you question. I will be writing the whole question, apologies in advance if it will be a lot of reading. A manufactures and sells three products X-Y-Z for which budgeted sale demand, unit selling price and unit variable costs are are follows: Product X Y Z Budget sale demand 550 500 400 Unit sale price 16 18 14 Variable cost Material 8 6 2 Labour 4 6 9 Contribution 4 6 3 The organization has existing inventory of 250 units of X and 200 units of Z which is quite willing to use up to meet the sale demand. All three products use the same direct materials and the same type of direct labour. In the next year the available supply of materials will be restricted to $4800 (at cost) and the available supply of labour $ 6600 (at cost) Determine which product mix and sale mix would maximise the organization profit in the next year. Solution: Define the which is the scars resource Product X Y Z Sale 550 500 400 Inventory 250 - 200 Production 300 500 200 Product Qty to produce Material Labour X 300 2400 1200 Y 500 3000 3000 Z 200 400 1800 Material supplied 4800 Labour supplied 6600 Shortfall (1000) 600 Material is the limiting factor. Rank the product in order of contribution earns of direct material Product X Y Z Contribution 4 6 3 material 8 6 2 0,5 1 1,5 Profit maximizing budget Product Unit Material/Cost Contribution T.C z 400 2 =800 1,5 1200 Y 500 6 =3000 1 3000 x 425 8=3400 0,5 1700 Why have total units been multiplied by contribution earn of direct material and not by the contribution per unit (4-6-3)? Thanks in advance Gabriella