11. Airborn travel and tours arrange trips and have a fixed cost of $1,000 per week. Their variable cost per trip can be represented by the function VC = X – 20 where X is the number of trips arranged. The price of a trip is $50. What is the break-even number of trips per week for this company?

Question

sasogeek · Answer

the variable cost turns out to be a function of number of trips which varies per week, obviously... how do i determine the value of X and hence, solve the problem?

sasogeek · Answer

break even = fixed cost / (selling price - variable cost)
break even = 1000 / (50-x+20)
break even = 1000/70-x

hence depending on the number of trips they have, they're break even point will either increase or decrease.

sasogeek · Answer

@hartnn

sasogeek · Answer

what do you think? can i leave my answer in terms of x or there's a value for x i'm not seeing? OR i could assume a value for x?

hartnn · Answer

i have not seen such question before, you have used all the given information , so i think the  answer will be in terms of X, 
is this calculus, in any way ??

hartnn · Answer

oh, this is economics...

sasogeek · Answer

not calculus, but it was an assignment by our computational math lecturer... :/

sasogeek · Answer

linear programming i suppose...

hartnn · Answer

found this in wiki, 'he break-even point (BEP) is the point at which cost or expenses and revenue are equal: there is no net loss or gain, and one has "broken even.'
donno whether it helps

hartnn · Answer

so can u find profit and loss ? 
then equate them, maybe u get an equation in X which you can solve

sasogeek · Answer

yeah i know what the break even point is, i just dunno about this question cos it says x is the number of trips a week but there's no clues as to how to determine x... unless maybe i work at that company lol :P

hartnn · Answer

1000+x-20= revenue = 50 = selling price 
so maybe u can find x from here, but i am not sure

hartnn · Answer

2nd opinion needed

sasogeek · Answer

hmmm, well finding x means x will now seize to be a variable...

hartnn · Answer

maybe for 1 break even point, there is one X, which we can find from the equation i wrote....

sasogeek · Answer

hmm, well that makes sense, so then the break even point is dependent on X... I guess I'll leave the answer in terms of X :/

hartnn · Answer

yeah, that was my first call, leave answer in X only....

sasogeek · Answer

ok thanks hartnn :) <3

hartnn · Answer

welcome ^_^

hartnn · Answer

though i didn't help much....

sasogeek · Answer

well you confirmed my work.. that's a lot xx