Question

SUPER URGENT!!!

Joel sells ice cream cones at the county fair. He has to rent the equipment for $36 and spend $0.52 on ingredients for each cone. What is the minimum number of ice cream cones Joel must sell at $1.40 each in order to make a profit?

Please explain ALL OF THE STEPS, or your answer is useless. Thanks!!

Answer 1

Denote by x the number of cones sold or produced.

Denote by C(x) the total cost.

Denote by R(x) the revenue made.

Denote by P(x) the net profit accumulated.

`C_(T)(x)=C_(fixed)+C_(variable) \: \\ C_(T)(x)=36+0.52x`

`R_(T)(x)=selling \: price \: x \\ R_(T)(x)=1.4x`

`P(x)=R_(T)(x)-C_(T)(x) \\ P(x)=1.4x-(36 + 0.52x) \\ P(x)=1.4x - 36 - 0.52x \\ P(x)=0.88x - 36`

If there exists profit, then P(x) has to be positive.

`P(x) > 0 \\ 0.88x - 36 > 0 \\ 0.88x > 36 \\ x > (36)/(0.88) \\ x > 40.90909 \\ x = 41`