Question

[3 pts]Suppose that new copies cost $100 and used copies cost $70. Assume the bookstorecurrently has 50 new copies and 50 used copies. What is the expected value of total revenuefrom the sale of the next 25 copies purchased

Answer 1

$1,975

Step-by-step explanation:

Given:

Cost of new copy = $100

Cost of used copy = $70

Total sales = 25 Copies

Note: Given question is incomplete, missing information is given below:

30% students want new copies,whereas 70% students wants used copies.

Computation of sale of new copies:

Total new copies = 25 × 30%

Total new copies = 7.5

Computation of sale of used copies:

Total used copies = 25 × 70%

Total used copies = 17.5

Computation of total revenue from sales:

Total revenue from sales = ($100 × Total new copies) + ($70 × Total used copies)

Total revenue from sales = ($100 × 7.5) + ($70 × 17.5)

Total revenue from sales = ($750) + ($1,225)

Total revenue from sales = $1,975

Answer 2

Expected Value = $2125

Step-by-step explanation:

Expected Value is the average value of all possible outcomes, weighted with the corresponding with the probability of each outcome

Formula : E {X} = Σ [ X. P(X) ]

Expected Value {Sales Revenue} = Σ [Total Revenue . P (Total Revenue)]

Case 1 : New Copies

• Sale Probability = Old Copies / Total Copies = 50 / 100 = 1/2
• 25 copies Total Revenue = 25 x price per copy = 25 x 100 = 2500

Case 2 : New Copies

• Sale Probability = New Copies/ Total Copies = 50/ 100 = 1/2
• 25 copies Total Revenue = 25 x price per copy = 25 x 70 = 1750

∴ Expected Value = (1/2) (2500) + (1/2) (1750)

= 1250 + 875 = 2125