The Radio Shop sells two popular models of portable sport radios, model A and mo

Question

The Radio Shop sells two popular models of portable sport radios, model A and model B. The sales of these products are not independent of each other (in economics, we call these substitutable products, because if the price of one increases, sales of the other will increase). The store wishes to establish a pricing policy to maximize revenue from these products. A study of price and sales data shows the following relationships between the quanity sold (N) and prices (P) of each model:

N(A) = 20 - o.62P(A) + 0.30P(B)

N(B) = 29 + 0.10P(A) - 0.60P(B)

*the letters in ( ) should be lower level letters

a. Construct a model for the total revenue and implement it on a spreadsheet.

b. What s the predicted revenue if P(A) = $20 and P(B) = $35? What if the prices are P(A) = $25 and P(B)=$50?

Explanation / Answer

Soln:

N(A) = 20 - 0.62P(A) + 0.30P(B)

N(B) = 29 + 0.10P(A) - 0.60P(B)

Total revenue = Price X quantity sold

TR = PA X[ 20 - 0.62P(A) + 0.30P(B)]

TRA = 20 PA - 0.62 PA 2 + 0.30 PA X PB

TRB = 29PB + 0.10 PA X PB - 0.60 PB 2

The predicted revenues for  P(A) = $20 and P(B) = $35

TRA = 20 X 20 - 0.62 X 202 + 0.30 X 20 X 35

TRA = 400 - 248 + 210

TRA = $ 362

TRB = 29X35 + 0.10 X 20X35 - 0.60 X 352

TRB = $ 350

If the prices are P(A) = $25 and P(B)=$50

TRA = 20 PA - 0.62 PA 2 + 0.30 PA X PB

TRA = $ 487.50

TRB = 29PB + 0.10 PA X PB - 0.60 PB 2

TRB = $ 75

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.