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Solving labour function

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Susan's utility function is U=(x+y)R^2; where x and y are the quntities of goods X and Y that she comsumes, and R is the number of hours of leisure that she has per day. Good X costs $4 and good Y costs $2 per unit. Her wage rate is $8 per hour nad she has 15 hours per day to allocate between labor and leisure.
She will:

a. consume equal amounts of X and Y
b. consume 10 units of units X
c. consume 20 units of Y
d. work 10 hours a day
e. consume twice as much of good X as of good Y

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Solving labour function is achieved.

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The problem is to be solved like this. We need to calculate MUx/Px and MUy/Py. The optimum point will be the point where two are equal. In this particular case The marginal rate of substitution for product X and Y ...

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