The weekly cost of manufacturing x telephones per week is found by a manufacturer to be C(x) = 500 + 20x = x^2 dollars. the telephone can be sold at a price p = $80 each. find the manufacturing break-even production level and for what production levels will the manufacturer experience a profit
calculus for business - cumhoc, Tuesday, January 17, 2012 at 11:31pm
telephones are not cheap to make, young whoppa
calculus for business - Steve, Wednesday, January 18, 2012 at 12:29am
breakeven occurs when cost = revenue
don't know whether you have + or minus x^2. On my keyboard, + and = are the same key, so I'll assume "+".
x^2 + 20x + 500 = 80x
x^2 - 60x + 500 = 0
(x-10)(x-50) = 0
So, for x between 10 and 50, cost is less than revenue.
This is a strange model. Usually as quantity increases, cost goes down.
Maybe you should have had C(x) = 500 + 20x - 1/x^2
or something. That would mean there's a fixed cost of $500 just for making phones, and a $20/phone cost for materials, say, and a decreasing manufacturing cost as quantity goes up. (efficiency of scale)
In that case, we'd have
500 + 20x - 1/(x^2+1) = 80x
That shows costs greater than revenue until x = 8.3 or so, then revenue is greater than costs.