The Good Buy Company manufactures DVD players. The marketing department finds th

Question

The Good Buy Company manufactures DVD players. The marketing department finds that if the company manufactures x DVD players per days its costs are and its revenues are C(x)= 150x+10,000 and its revenues are R(x)= -2x^2+600x.   

a. On the same set of axis graph both functions and clearly label each function. State the window used.
b. Find the break-even points, algebraically, graphically, or numerically and show work to support your answer. State your solution in a complete sentence.

c. How many DVD players should Good Buy produce in order to make money each day?

d. How many DVD players should the firm make in order to maximize revenue?

e. What is the equation for the profit function?

f. How many DVD players should the firm make in order to maximize profit?

Explanation / Answer

break even point is when cost=revenue ie
c(x)=150x+10,000=R(x)=-2x^2 +600x.
150x+10,000=-2x^2 +600x.
solving we get x=25 or x=200
Both are break ven points

b) profit function=revenue-cost
(-2x^2 +600x)-(150x+10,000)
p(x)= -x^2+225x-5000

c) maximum prifit is when dp/dx=0

dp/dx=2x-225=0
when x=112.5
say x=113
the number of dvd players they must sell to maximize profit=113


max profit is obtained when we put x=113 in p(x) above
we get max profit as 7656

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