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,

- Total supply of books = 40, that is,

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

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

- 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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