SOLUTION: After leaving a fulfilling career as a singer, Sally decides to venture out into the world of necklace sales. The cost of producing x necklaces is given by the function C(x) = 1.3x

Question 189942: After leaving a fulfilling career as a singer, Sally decides to venture out into the world of necklace sales. The cost of producing x necklaces is given by the function C(x) = 1.3x + 275. The necklaces can be sold on E-bay for $10 each.
(a) What are the fixed costs?
(b) Find the revenue and profit functions.
(c) Find the break-even point.
(d) If Phil manages to sell 500 DVD�s per month, what will his yearly profit be?

Answer by cutepiscean5(19) (Show Source): You can put this solution on YOUR website!
After leaving a fulfilling career as a singer, Sally decides to venture out into the world of necklace sales. The cost of producing x necklaces is given by the function C(x) = 1.3x + 275. The necklaces can be sold on E-bay for $10 each.
(a) What are the fixed costs?
>>> The fixed costs will be determined from the function C(x) = 1.3x + 275. we know that by looking at the cost function the fixed cost is 275.
(b) Find the revenue and profit functions.
>> --- the revenue function will be determined by the selling price of x necklaces.
so if 1 necklace is sold for $10, x necklaces will be sold for $ 10x.
-- For the profit function, we know that Profit = Selling price - Cost price
= 10x - (1.3x + 275)
= $ (8.7x - 275)

(c) Find the break-even point.
The break-even point is the point where there is no profit, no loss. that means the selling price is same as the cost price.
so, for break-even, 10x = 1.3x + 275
=> 10x - 1.3x = 275
=> 8.7x = 275
or, x = 31.60 which approx s to 32 necklaces, the break even is 32 necklaces
(d) If Phil manages to sell 500 DVD�s per month, what will his yearly profit be?
>>> I could not get how is this question related to the previous one??
Please have a look at the rest of the questions..
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