A manufacturer found hat the sales figure for a certain item depended on the selling price. The market research department found that the maximum number of items that could be sold was 20,000 and that the number actually sold decreased by 100 for every 1p increase in price. The total cost of production of the items consisted of a set-up cost of 200 euros plus 50p per item manufactured. Show that the profit y pence as a function of the selling price x pence is y=25000x-100x^2-1020000
What price should be adopted to maximize profits, and how many items are produced?