Need help getting started on partial differentiation problem

I am struggling with the following question. 

A monopolistic firm has the following demand and cost functions for each of its two products x and y :  

Qx=40-2Px-2Py

Qy= 35 - Px - Py

C = Qx2 + 2Qy2 + 10 

where Px and Py are the prices of the goods x and y respectively.

(a) Find the output levels of x and y that maximise the profit and confirm the existence of a unique maximum (note that for each product the revenue, R, is such that, R = PQ).

(b) Find also the profit-maximizing prices and the maximum profit.

Any help would be appreciated, I honestly have no idea where to begin.

Student X

Here’s getting you started:

Let the profit function f = PxQx + PyQy - C

Rewriting both Px and Py in terms of functions of Qx and Qy, 

ie Px = h( Qx, Qy) and Py = g (Qx, Qy)

Substitute this together with the cost function C into f to obtain an expression purely in terms of Qx and Qy.

For output levels which maximise profit, the partial derivatives of f wrt Qx and f wrt Qy must be equal to zero.

From there, solve for Qx and Qy accordingly.

At this point you will not be too far from obtaining Px, Py and the profit f.

Hope this helps. Peace.

Best Regards,

Mr Koh