Question 326857: After leaving a fulfilling career is a math teacher, Phil decides to venture out into the world of DVD sales. The cost of producing x DVD’s is given by the function C(x) = 1.3x + 275. The DVD’s 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 jessica43(140)   (Show Source):
You can put this solution on YOUR website! (a) Fixed costs are the costs Phil has to pay even if he doesn't produce any DVDs, or in otherwords, if x=0 in the cost function:
C(0) = 1.3(0) + 275
C = 275
So the fixed cost is $275.
(b) The revenue function is the price sold times the quantity sold. In this problem, we know that DVDs are sold at $10 each:
R = 10x (where x= quantity of DVDs)
The profit function is revenue less costs, or:
P = R - C
P = 10x - (1.3x + 275)
(c) The break-even point is the point where Phil is making no profits, but is also incurring no losses. This is when revenue = costs, or profits equal zero. So set your profit function equal to zero and solve for x:
P = 10x - (1.3x + 275)
0 = 10x - 1.3x - 275
0 = 8.7x - 275
275 = 8.7x
x = 31.609
So the break even point is when Phil produces and sells approximately 31.6 DVDs.
(d)This question is tricky because there are two different answers depending on how you interpret the fixed costs. If the fixed cost of 275 is a yearly cost, that means they will only pay the 275 once. You would then figure out how many DVDs he would produce in a year (500*12=6000 DVDs per year) and plug that into the profit equation for x and solve for P. In this case, P = $51,925.
If the cost equation is a monthly cost equation, that would mean Phil would have to pay the fixed cost of 275 every month. So you would plug 500 into the profit equation to find out his profit for one month ($4,075 per month profit). Then you would multiply this monthly figure by 12 to find the profit for a year: 4075*12 = $48,900.
Hopefully this didn't confuse you too much. I just want you to know that your yearly profits could be $51,925 or $48,900 depending on how you read the problem. Both answers are correct, so use what makes more sense to you.
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