Smelly Perfume Company manufactures and distributes several different products. The company currently uses a plantwide allocation method for allocating overhead at a rate of $$7$ per direct labor hour. Cindy is the department manager of Department $C$ which produces Products $J$ and P$.$ Department $C$ has $$16,200$ in traceable overhead. Diane is the department manager of Department $D$ which manufactures Product $x.$ Department $D$ has $$11,100$ in traceable overhead. The product costs $($per case of $24$ bottles$)$ and other information are as follows:

If Smelly changes its allocation basis to machine hours, what is the total product cost per case for Product $P?$