Calculate the allocation of outputs across the two periods

Calculate the allocation of outputs across the two periods

Suppose the MWTP in periods 1 (now) and 2 (one year from now) is given by P = 8-0.4q. Marginal extraction cost = $2. r = 15%. The available supply is 20 units. Calculate the allocation of outputs across the two periods that maximizes the present value of the net benefits for the use of the resources.

The only problem I am having is finding q1 and q2. I just completed a problem with the same steps, but q1 and q2 were given. Is there a way to figure this out mathematically, or should I just be guessing? Please help!

All I have so far is:

Max Willing to Pay- P=8-0.4q

Marginal Extraction Cost- $2

r=15% or 0.15

Available Supply- 20 units

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