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Exercise 6.3: Assume that the hospital is a monopolist with a demand function that incorporates quality...

Exercise 6.3: Assume that the hospital is a monopolist with a demand function that incorporates quality of care as well as quantity. Quality enters into both the demand and cost functions according to P = 100 - 3x + 4Y^(1/2) and C = 4x^2 + 10x + y, where P is the price of hospital care, x is the quantity of hospital care, y is the quality of hospital care, and C is the total cost. Compute the hospital's profit maximizing output, quality, price, revenue, and profit.

THESE ARE THE ANSWERS BUT WHAT IS THE STEP BY STEP SOLUTION?
we solve the system to find x*=15 and y*= 900. By using these optimal values in the price, revenue and profit functions we find: p = $175, revenue = $2,625 , profit = $675

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