Question

At Carla's taco stand, each taco costs $2.10 to make and she sells each one for $5.75; and her daily fixed costs are $180. Let x-the number of tacos that are made and sold. Assume that all tacos that are made are also sold. A) The revenue is defined as the total money that customers paid. Write a function for R(x), the revenue from selling tacos. B) Write a function for C(x), the total cost of making x tacos: C) Write a function for P(x), the profit from selling x tacos (simplify your answer) D) How many tacos must be sold for Carla to break even on a given day? Give your answer as a whole number. (Breaking even means zero profit) E) At the end of one day, there was $690 in the cash register. What were her costs and her profit for the day?

Answer 1

Answer A:

Let x be the number of tacos that are made and sold in a day.

Sale price of each taco =$5.75

Hence:

R(x) = $5.75 * x = 5.75x

R(x) = 5.75x

Answer B:

Variable cost per taco = $2.10

Total variable cost for making x tacos = $2.10 * x

Fixed cost per day = $180

Total cost for making x tacos = $180 + $2.10 * x

Hence:

C(x) =180 +2.10x

Answer C:

Profit = Total Contribution - Fixed cost = ($5.75 - $2.10) * x - $180

=3.65x - 180

Hence:

P(x) = 3.65x -180

Answer D:

Break-even in units = Fixed cost / Contribution per unit = 180 / (5.75 - 2.10) = 49.31 = 49

Break-even in units = 49

Answer E:

As all tacos that are made are sold and assuming all cash transactions:

690 = 3.65x -180

=> x = (690 +180) / 3.65 = 238.36 tacos

Total cost = 238.36 * 2.10 + 180 = $681

Hence:

Profit = $690

Cost = $681