Suppose a product can be produced either using newly harvested materials according to:M C$1=2$q$1$

AND can also be produced using recycled materials according to:

M C$2=4+$ q$2$

$$ a$)$ Suppose demand is given by P $=152($q$1+$ q$2).$ Find the relationship between q$1$ and q$2$ that

results in profit maximization for the firm. $(4$ pts$)$

$$ b$)$ Use this relationship to put demand in terms of only q$2.$ Then solve for the optimal number of

units produced using recycled materials. $(4$ pts$)$

$$ c$)$ How many units will be produced using the newly$-$mined material if the firm acts optimally? $(4$

pts$)$

$$ d$)$ How would we expect this allocation to change if M C$2=15+$ q$2$ instead? $($Do not need to answer numerically$)(2$ pts$)$

$4$