Sona Corp manufactures fabric bags. It manufactures two sizes of bags: Small size and Large size using the same production facility. The following information is available for the forthcoming month: Particulars Small size Large size Estimated demand (units) 220,000 175,000 Selling price per unit $18 $22 Variable cost per unit $8 $10 Machine hours required per batch 15 25 Both sizes of bags can be produced only in batches of 100 units. Sona Corp aims to have no inventory of finished goods as it has a very small warehouse where most of the space is occupied by the raw materials required to produce the bags. Hence, inventory build-up of finished goods is not possible from one accounting period to another. The total fixed costs for each level of production and directly attributable to Small size bags and Large size bags are as follows: Relevant rage of output Fixed costs for Small size bags Large size bags Up to 100,000 units $600,000 $550,000 100,001 to 200,000 units $1,350,000 $1,220,000 200,001 to 300,000 units (Maximum possible level) $1,870,000 $1,550,000 Each month, the production facility of Sona Corp has 75,000 machine hours at its disposal. 

Required: 

(a) Determine the contribution per unit of the limiting factor for both small and large size bags. Also, determine the maximum contribution achievable based on the available quantity of the limiting factor. 

(b) Determine the best product mix (quantities of Small size bags and Large size bags) to be produced and sold to achieve the maximum profit in the forthcoming month. Justify your answers by providing all necessary calculations.