Ren and Jasmine decide to form a partnership. Ren will contribute RM$500,000$ to the partnership, while Jasmine will contribute only RM$90,000.$ However, Jasmine will be responsible for running day to day operations of the partnership, which are anticipated to require about $45$ hours per week. In contrast, Ren will only work five hours per week for the partnership. The two partners are attempting to determine a formula for dividing partnership net income. Ren believes the partners should divide income in the ratio of $6$:$4$ favoring Ren, since Ren provides the majority of the capital. Jasmine believes the income should be divided $6$:$4$ favoring Jasmine, since Jasmine provides the majority of effort in running the partnership business.

Required:

Recommend with proper arguments to the partners, Ren and Jasmine in developing a method for dividing income.