A manufacturer can produce radio at a cost of $10 apiece and estimated that if they are sold for x dollars, consumers will buy approximately 80-x radio each month. Express the manufacturer's monthly profit as a function of the price x, graph this function and determine the the price at which the manufacturer's profit will be greatest .
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Since we know profit to be equal to total revenue minus total cost, we also know our cost to be $10 and the quantity that’s the amount the consumers are buying and it is (80-x) and also the selling price is x . We then deduce our total revenue to be price x quantity and that is x(80-x) . That would give us (80x - x^2). We then come to the profit function knowing our total revenue. Therefore the profit function becomes (-x^2 + 80x - 10) .. we can then find the points of this quadratic equation by solving it. After getting the points we then find the corresponding y intercepts and draw the graph of it. The turning point of the graph becomes the greatest profit price of the producer .
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