Question

Can someone please help me set up this problem?
"To produce x units of a religious medal costs C(x)=12x+133. The revenue is R(x)=31x. Both cost and revenue are in dollars.
A. Find the break even quantity
B. Find the profit from 480 units
C. Find the number of units that must be produced for a profit of $190.
I'm having difficulty setting the problem up. I thought a profit function was p(x)=R(x)-C(x) but I keep getting the wrong answer. TIA!

Answer 1

p(x) = R(x) - C(x)
p(480) = 31*480 - 12*480+133
p(480) = 480*(31-12) + 133
p(480) = 480 *(19) + 133
p(480) = $9253

Answer 2

Thanks. Do you know how to find c?

Answer 3

there was an error above, $133 takes away profit
rather than adding to profit

p(480) = 31*480 - 12*480-133
p(480) = 480*(31-12) - 133
p(480) = 480 *(19) - 133
p(480) = 9120 - 133
p(480) = $8987 do you have possible solutions?

Answer 4

I basically missed the second term in C(x)
C(x)=12x+133
-C(x)= -12x -133

Answer 5

Awesome! Thanks so much!

Answer 6

for c) we have the profit given and look for number x

p(x)=$190 = R(x) - C(x)
190 = 31x - 12x - 133
190 = 19x -133 [[at this point we see that 19x must be greater
[[ than 133 PLUS 190 to cancel that and then
[[ make further profit
190+133 = 19x
323 = 19x
x=17

check if 17 is the correct required manufacture #:
p(17) ?= $190
p(17) = 19x-133
p(17) = 19*17 - 133
p(17) = 323 - 133
p(17) = $190

it is necessary to produce 17 medals on a given (day?).
to have a profit of $190