ll T-Mobile 8:25 PM 96% Section 23 - Exercises (answers follow) e numbers z and y such that z +y 150 and zy is maximized su 1. Find non-negative 2. You are to enclose a rectangular garden having an area of 3,600 square meters and surround it by a fence. How can this be done using the least amount of fencing? 3. What are the dimensions of an open (no top) rec tangular box that has a square base, a capacity of 32,000 cm3, and is constructed using the least amount of material? 4. If a manufacturer charges p(x) dollars per item, where p(r) = 4-121 then thousand ite will be sold (a) Find an expression for the total revenue from the sale of x thousand items (b) Find the value of z that leads to maximum revenue. (c) Find the maximum revenue. oduction of widgets the marginal revenue and marginal cost (in thousands of dollars + 10 per item) for producing z widgets are given by R()70-z and ()0.122 +4 (a) What is the number x at which these are equal? (b) Interpret the result: for what value of x is profit maximal? 6. Ifx units are produced, the cost of production is C(z) 400 + 2x+ 0.05x2. In order to sel units it is known that the price per unit should be p(x) production level that will maximize profit 10- dollars. Find the 7. A cylindrical can without a top is to be made to have volume 100 cubic centimeters. Find the 8. Find the dimensions of the rectangle of largest area that can be inscribed in a semicircle of 400 radius of the base and the height of the can which wil minimize the cost of the can radius 6. W the origin, of radius r is y = Vr2- hat is the area of the rectangle? (Note: The equation of a semicircle, centered at 2 9. Draco spent $1000 to purchase some stock. He tracked the performance of his investment for 20 days. A function that shows the value of his stock V (dollars) at time t days after his purchase is given by V(t)--3t8260t+1000. At what time did the investment have the most value? 10. Barry runs a chal k manufacturing company. It costs the company $1 to make each box of chalk. When the company sells the c million boxes per year. Find the price that Barry should charge for a box of chalk in order to maximize his annual profit halk for $p per box, they are able to sell q(p) p +1 p3 11. At what point on the curve y 3-32 +3 does the tangent to the curve have the smallest slope? What is the slope at this point? 192