Question

In: Math

Your company is considering two products for a new market. The probability distribution for the demand...

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?

Solutions

Expert Solution

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


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