AMS recently instituted an in-house recycling program. The benefits of this prog

Question

AMS recently instituted an in-house recycling program. The benefits of this program include not only the benefits to the environment of recycling but also the goodwill generated by AMS's leadership in this area. The costs of recycling include all of the energy, labor, and space required to do the recycling. Suppose these benefits and costs are given by B(Q)=100Q-2Q^2 and C(Q)=2Q.(Note that MB=100-4Q, and MC=2.) a. What level of Q maximizes the total benefits of recycling? b. What level of Q minimizes the total costs of recycling? c. What level of Q maximizes the net benefits of recycling? d. What level of recycling is optimal? Why?

Explanation / Answer

perfectly solved..with all steps and details..!!

a. MB is the slope of the benefits function. The max benefit will occur when
MB =100 - 4Q = 0
Q = 25
Plug this value of Q into the benefits function:
B(25) = 1250 this is the max benefits.

b. Since C is linear (constant slope, MC = 2) the minimum cost will be Q = 0, C(0) = 0

c. Net benefit will be B(Q) - C(Q). Let's call this N(Q)
N(Q) = 98Q - 2Q^2 and MN = 98 - 4Q
Same process now as with a.
0 = 98 - 4Q
Q = 49/2 or 24.5 (round as necessary, I'm assuming you can't have a half unit).
N(24) = 1200 (N(25) = 1200 as well, your pick)

d. The answer is c. is optimal since you need to balance the potential benefits against the cost.

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