3. (6 pts) Th management Acrosonic plans to market e ElectroStat, an electrostat

Question

3. (6 pts) Th management Acrosonic plans to market e ElectroStat, an electrostatic speaker system. The marketing department has determined that the demand function for these (0 S x S 20,000) p 0.04x 800 speakers is where p denotes the speaker's unit price in dollars and x denotes the quantity demanded Acrosonic's production department estimates that the total cost (in dollars) incurred. in manufacturing X El ectro Stat speaker systems in the first year of production will be COx 200x 300,000 a) Find the revenue and profit functions, RCx) and POx). R (x) POx) b) Find the marginal revenue and profit functions, R'Ox and P'(x). R'(x) P'Ox) c) Find P 5000) and explain in words) what it represents in context of this problem. Answer:

Explanation / Answer

a)R(x)=p*x=-0.04x^2+800x

P(x)=R(x)-C(x)=-0.04x^2+800x-200x-300000=-0.04x^2+600x-300000

b)R'(x)=-0.08x+800

P'(x)=-0.08x+600

c)P'(5000)=-0.08*5000+600=200.

This means that on producing the 5000th unit the profit increases by $200 over the profit from 4999 units.

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