5. Ollivanders is a wand shop for wizards in Hogwarts. It has been estimated that when x wands are produced per week, the market price of each wand (in Galleons) will be p(x) = 21 - * and the total cost (in Galleons) will be C(x) = x² + 5x + 40. 3. Apart from the total cost, their government, the Ministry of Magic, imposes a tax of t Galleons for each wand produced. This tax becomes an additional cost item to the shop. (a) Suppose thatt is not yet known. Show that the profit of Ollivanders is maximized when 5. x = 10 -t. 8 (b) Assume that Ollivanders will always act so as to maximize profit. How much tax t should the Ministry of Magic charge per wand to maximize tax collections? (c) From the results in (a) and (b), find the final profit of the wand shop. What can you conclude?

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