Answer and Explanation:
FC = Fixed Cost = $100,000
VC = Variable Cost = $34 per doll
SP1 = Sales Price (during holiday season) = $42 per doll
SP2 = Sales Price ( January – off season ) = $10 per doll
Average demand :
Demand = 60,000
Mean = 60,000
Standard Deviation = 15,000
Demand follows normal probability distribution
Tentative Production forecast = 60,000 dolls
Calculated Production forecast =
Average Profit:
Profit standard Deviation:
Maximum Profit:
Profit = Sales – (Variable Cost + Fixed Cost)
During the holiday season,
For 40,000 dolls
Soales = 40,000 * 42 = $1,680,000
próofit = $1,680,000 – (VC+FC)
VC = 34*40,000 = 1,360,000
FC = Fixed Cost = $100,000
Total Cost = VC + FC
1,360,000+100,000 = $1,460,000
Profit = 1,680,000 – 1,460,000
= $220,000
Maximum Profit = $220,000
Average Profit:
Off season sale price * Demand =
$10*40,000
= $400,000
average sales = ($400,000 + 1,680,000 ) / 2
=$2,080,000/2
= $1,040,000
Average profit = 1,040,000 – 73,000
= $967,000
Probability of a loss:
Probability = 1 - F(Z)
where F(Z) = (Qty – Miu / SD)
F(Z) = 60,000 - 40,000 / 15,000
=20,000/15,000
= 1.33
Absolute value of (1 – F(Z)
= 0.33
Probability of loss = 0.33 or 1/3
Possibility of a Shortage = 1 – Probability of loss = 1 – 1/3 = 2/3
