A firm is planning to manufacture a new product. The sales department estimates that the quantity that can be sold depends on the selling price. As the selling price is increased, the quantity that can be sold decreases. Numerically they estimate: P = $35.00 - 0.02Q, where P =selling price per unit, Q = quantity sold per year. On the other hand, the management estimates that the average cost of manufacturing and selling the product will decrease as the quantity sold increases. They estimate C = $4.00Q + $8000, where C = cost to produce and sell Q per year. The firm's management wishes to produce and sell the product at the rate that will maximize profit, that is, where income minus cost will be a maximum. What quantity should the decision makers plan to produce and sell each year?
A loan of $10,000 is to be repaid over a period of eight years. During the first four years, exactly half of the loan principal is to be repaid (along with accumulated compound interest) by a uniform series of payments of A1 dollar per year. The other half of the loan principal is to be repaid over four years, with accumulated interest, by a uniform series of payments of A2 dollar per year, If i=9% per year, what are A1 and A2?
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