Question

The Rejuvo Corp. manufactures granite countertop cleaner and polish. Quarterly sales Q is a random variable with a mean of 20,670 bottles and a standard deviation of 2,110 bottles. Variable cost is $14 per unit and fixed cost is $172,540. (a) Find the mean and standard deviation of Rejuvo’s total cost.

Mean $

Standard deviation $

(b-1) If all bottles are sold, what would the selling price have to be to break even, on average? (Round your answer to 2 decimal places.) Selling price $

(b-2) If all bottles are sold, what would the selling price have to be to make a profit of $29,510? (Round your answer to 2 decimal places.) Selling price $

Answer 1

The mean of total cost is (Mean of bottle*Variable cost per unit) + Fixed cost
Calculation of mean of total cost
Mean of total cost = (20,670*14) + 172,540
Mean of total cost		$461,920
Standard deviation of total cost = Standard deviation*Variable cost per unit
Standard deviation of total cost = 2110*14
Standard deviation of total cost			29540
The mean of total cost of $461,920 and standard deviation is $29,540
b-1
At the break even Total revenue - Total cost = 0
Therefore, we have following equation
20,670*P - 461920 = 0
20670P = 461920
P	461920/20670
P	22.35
The selling price of the bottle on average should be $22.35
b-2
If we want profit of $29,510, we get the equation as
Total revenue - Total cost = 29510
20,670*P - 461920 = 29510
20670P = 29510+461920
P	491430/20670
P	23.78
The selling price of the bottle on average should be $23.78