In: Math
Your company is considering two products for a new market. The probability distribution for the demand for the two products is presented in the table below. Q(A) and Q(B) are the possible quantities of each product that could be sold. P(A) and P(B) are the probabilities of selling the corresponding quantities.
Q(A) |
P(A) |
Q(B) |
P(B) |
10000 |
0.15 |
10000 |
0.25 |
30000 |
0.20 |
30000 |
0.30 |
50000 |
0.40 |
50000 |
0.35 |
60000 |
0.25 |
60000 |
0.15 |
You have the following additional information: The projected selling price for DESIGN "A" is $60. The fixed cost of its production is$75,000. Its variable cost is $35 a unit. The selling price for DESIGN "B" is $80. Its fixed cost of production is $110,000. Variable cost of production is $48 a unit.
Which project is expected to be more profitable?
Expected Profit = (Unit selling price - Variable Cost per unit) x Expected selling Quantity - Fixed Cost
Expected selling Quantity for the Design "A"
Q(A) | P(A) | Q(A)P(A) |
10000 | 0.15 | 1500 |
30000 | 0.2 | 6000 |
50000 | 0.4 | 20000 |
60000 | 0.25 | 15000 |
E(Q(A)=42500 |
Expected selling Quantity for the Design "A" = 42500
Unit Selling price DESIGN "A" = $60
Variable Cost per unit for DESIGN "A" = $35
Fixed cost of DESIGN "A" production = $75,000
Expected Profit For DESIGN "A"
= (Unit selling price - Variable Cost per unit) x Expected selling Quantity - Fixed Cost
=(60-35)*42500 - 75000 = (25)*42500 - 75000 = 1062500-75000=987500
Expected Profit For DESIGN "A" = $ 987,500
Expected selling Quantity for the Design "B"
Q(B) | P(B) | Q(B)P(B) |
10000 | 0.25 | 2500 |
30000 | 0.3 | 9000 |
50000 | 0.35 | 17500 |
60000 | 0.15 | 9000 |
E(Q(B))=38000 |
Expected selling Quantity for the Design "B" = 38000
Unit Selling price DESIGN "B" = $80
Variable Cost per unit for DESIGN "B" = $48
Fixed cost of DESIGN "B" production = $110,000
Expected Profit For DESIGN "B"
= (Unit selling price - Variable Cost per unit) x Expected selling Quantity - Fixed Cost
=(80-48)*38000 - 110000 = (32)*38000-110000 = 1216000-110000=1106000
Expected Profit For DESIGN "B" = $1,106,000
Expected Profit For DESIGN "B" = $1,106,000 is more than Expected Profit For DESIGN "A" = $ 987,500
Hence
Project "B" is expected to be more profitable