Question

The Rejuvo Corp. manufactures granite countertop cleaner and polish. Quarterly sales Q is a random variable with a mean of 25,000 bottles and a standard deviation of 2,000 bottles. Variable cost is $8 per unit and fixed cost is $150,000. (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? Selling price $ (b-2) If all bottles are sold, what would the selling price have to be to make a profit of $20,000? (Round your answer to 2 decimal places.) Selling price $

Answer 1

Answer:

Mean of total cost = $350,000

Standard deviation of total cost = $16,000

Selling price of the bottle on average should be $14

The selling price of the bottle on average should be $14.8

Explanation:

Mean of total cost =((Mean of bottle × Variable cost per unit) + Fixed cost

Mean of total cost = 25,000 × $8 per unit + $150,000

= $200,000 + $150,000

= $350,000

Standard deviation of total cost = Standard deviation × Variable cost per unit

= 2,000 × $8

= $16,000

b-1  The break even Total revenue - Total cost = 0    

So, we have given equation

25,000 × P - $350,000 = 0

25,000P = $350,000

P = $350,000 ÷ 25,000

= $14

b-2 For making profit of $20,000, the equation

Total revenue - Total cost = $20,000

25,000 × P - $350,000 = 20,000

25,000P = 20,000 + $350,000

25,000P = $370,000

P = $370,000 ÷ 25,000

= $14.8

The selling price of the bottle on average should be $14.8