10. Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), of producing x units are in dollars. R(x) = 40x - 0.1x", C(x) = 6x + 10 In order to yield the maximum profit of $_ units must be produced and sold. (Simplify your answers. Round to the nearest cent as needed.) 11. Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), are in thousands of dollars, and x is in thousands of units. R(x) = 7x - 3x". C(x) = x - 4x + 4x+1 The production level for the maximum profit is about units. (Do not round until the final answer. Then round to the whole number as needed.) The profit is about $ "Do not round until the final answer. Then round to the whole number as needed.) 12. An apple farm yields an average of 40 bushels of apples per tree when 24 trees are planted on an acre of ground. Each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. How many trees should be planted on an acre in order to get the highest yield? In order to get the highest yield, trees should be planted on an acre. 13. A rectangular box with a volume of 320 ft" is to be constructed with a square base and top. The cost per square foot for the bottom is 20c, for the top is 15e, and for the sides is 2.5p. What dimensions will minimize the cost? What are the dimensions of the box? The length of one side of the base is (1) The height of the box is (2) (Round to one decimal place as needed.) (1) Ofta. (2) Of. Oft. Oft . 14. A retail outlet for calculators sells 720 calculators per year. It costs $2 to store one calculator for a year. To reorder, there is a fixed cost of $5, plus $2.75 for each calculator. How many times per year should the store order calculators, and in what lot size, in order to minimize inventory costs? The store should order calculators times per year to minimize inventory costs. (Simplify your answers.) 15. An open-top cylindrical container is to have a volume 2744 cm. What dimensions (radius and height) will minimize the surface area? The radius of the can is about cm and its height is about cm. 'Do not round until the final answer. Then round to two decimal places as needed.]