Question

The Rejuvo Corp. manufactures granite countertop cleaner and polish. Quarterly sales Q is a random variable with a mean of 23,790 bottles and a standard deviation of 2,150 bottles. Variable cost is $10 per unit and fixed cost is $123,750. (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 $21,695? (Round your answer to 2 decimal places.)

Answer 1

1.
Total Cost=Q*10+123750
Standard Deviation^2=E(Q^2)-mean^2
=>E(Q^2)=2150^2+23790^2
Mean of Total cost=E(Q*10+123750)=10*E(Q)+E(123750)=10*23790+123750=361650

Variance of Total cost=E(TC-E(TC))^2=E((10*Q+123750)^2)-361650^2=E(100*Q^2+123750^2+20*Q*123750)-363450^2=100*E(Q^2)+123750^2+20*123750*23790-361650^2=100*(2150^2+23790^2)+123750^2+20*123750*23790-361650^2=462250000

Standard Deviation of Total Cost=sqrt(462250000)=21500

2.
=123750/23790+10=15.20176545

3.
=(21695+123750)/23790+10=16.11370324