Math 211 S101 Quiz VI (25 pts) Name____________________________________ 1) Find the absolute maximum and absolute minimum (if any) of the function 1 f ( x) x3 9 x 2 on the interval 1 x 4. 3 2) Find the absolute maximum and absolute minimum (if any) of the function f ( x) x 2 16 on the interval x 0. x 3) If the price p(q) at which q units of a product can be sold is p(q) 37 2q, and the total cost C (q ) of producing q units is C ( q) 3q 2 5q 75, then find the revenue function R(q), the profit function P(q), and the value of q for which the profit P(q) is maximized. Find the Average Cost A(q) the value of q for which the Average Cost is minimized. C (q) and determine q 4) A store has been selling a popular computer game at the price of $40 per unit, and at this price, players have been buying 50 units per month. The owner of the store wishes to raise the price of the game and estimates that for each $1 increase in price, 3 fewer units will be sold each month. If each units costs the store $25, at what price should the game be sold to maximize profit? 5) A store expects to sell 2000 bottles of perfume this year. The perfume costs $25 a bottle, the ordering fee is $10 per shipment, and the cost of storing the perfume is 64 cents per bottle per year. The perfume is consumed at a constant rate throughout the year and each shipment arrives just as the preceeding shipment is being used up. Storage costs are based on the average inventory. How many bottles per shipment should the store order in order to minimize costs