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Section Assignment #5 -Done In Class on Thursday 2/27

You have a small business which sells boxes of greeting cards. Let \(x\) be the demand for boxes of cards and assume that it is inversely proportional to the square of the price \(p\) of a box of cards.
  1. If you charge $16 per box of cards, 100 boxes are sold. Find an expression for the price \(p\) of a box of cards as a function of the demand \(x\).

    2. Your initial investment for the business is $750 and it costs you $5 for each box of cards.
  2. Find an expression for the cost \(C\) of your business as a function of demand.

  3. Find an expression for the revenue \(R\) of your business as a function of demand.

  4. Find an expression for the profit \(P\) of your business as a function of demand. (Recall, Profit= Revenue- Cost.)

  5. According to your answer to part d, determine which values of demand lead to an increase in profits, and which values of demand lead to a decrease in profits.

  6. What values of demand and price will maximize your profit?