Maximizing LTC reimb. -formula

Dtail

Give me a museum and I'll fill it. (Picasso) Give me a forum ...
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Okay for you math folks out there.

With time on my hands, I realized that my parents are receiving more monies for the home care which my father is receiving than the payouts they are making.

TASK:
Can someone devise a formula which would maximize the net income on a monthly basis?

Input:
Caregiver costs: $21 per hour for the first 40 hours weekly. $31.50 per hour after the first 40 hours.

LTC reimbursement:

Insurance company 1: reimburses a maximum of $1,860 monthly. It is purely based on cost, so 40 hours = $840, 100 hours would be limited to $1,860. There are no daily limits.

Insurance company 2: reimburses a maximum of $115 daily. So 4 hours would be $84 and 6 hours would be limited to $115. There is no maximum per month.

Thus I noticed in the first 2+ months, my parents netted over 2k.
My father typically receives ~ 40 hours weekly of service, but there is some flexibility.

No care decisions would be made on this response; just curious on the mathematical maximization formula.

Hey something to do besides worrying about the virus.
 
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