Lawn Products produces two products (X and Y) and a by-product (Z) from a joint process using a raw material (Alpha). The company chooses to allocate the costs on the basis of the physical quantities method.

Last month, it processed 12,000 pounds of Alpha at a total cost of $88,000. The output of the process consisted of 37,350 units of product X, 45,650 units of product Y, and 6,000 units of by-product Z. By-product Z can be sold for $16,300. This is considered to be its net realizable value, which is deducted from the processing costs of the main products.

Required:
What amount of joint costs should be assigned to each of product X and product Y?