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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?

check_circleAnswer
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...

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