Banksy Ltd manufactures two products, the first product is a bag with a specific print on them and the second product is a series of postcards (sold in a pack of 10) with the same print on them. Information regarding the costs associated with both the bags and postcards is below:

Bags: has a selling price of $30, and variable costs of $12 per unit. The bags need to be put through the printing machine once sewn and require 1.5 hours on the machine.

Postcards: the pack has a selling price of $10, and variable costs of $5 per unit. The postcards also need to be put in the printing machine for only 15 minutes per pack.

Maximum demand is 200 units per product and the printing machines capacity is limited to 100 hours.

Determine how the 100 hours of printing machine time should be allocated to the two products to provide the most profitable mix. Show all workings.