  Your company receives 40 excess copies of a book. You plan to sell these books in two markets: directly in the store or sell them on ebay. Here are the two demand equations: Store Demand: P_S = 200 – 2Q_S PS​=200–2QS​ Ebay Demand: P_E = 250 – 5Q_E PE​=250–5QE​ If your goal is to maximize total revenue, how many books will you sell on ebay?

Question

Your company receives 40 excess copies of a book. You plan to sell these books in two markets: directly in the store or sell them on ebay. Here are the two demand equations: Store Demand: P_S = 200 – 2Q_S PS​=200–2QS​ Ebay Demand: P_E = 250 – 5Q_E PE​=250–5QE​ If your goal is to maximize total revenue, how many books will you sell on ebay?

Step 1

It is given that,

1. Total supply of books = 40, that is,

Quantity of books at ebay (Qe) + Quantity of books at store (Qs) = 40 or Qs = 40 – Qe.

1. Demand at store (Ps) = 200 – 2Qs and Demand at ebay (Pe) = 250 – 5Qe

1. Total Revenue (TR) can be estimated as TR = Ps * Qs + Pe * Qe
Step 2

Step 2

Now estimate TR by using above equation

TR = (200 – 2Qs) * Qs + (250 – 5Qe) * Qe

Furthermore, differentiate TR subject to Qs + Qe = 40

Step 3

Use LaGrange to determine the respectiv...

Want to see the full answer?

See Solution

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in 