MAC 2311 worksheet # 10 strategy guide The following elements need to be a part of solutions for optimization problems. ( max mins ) : 1) A carefully labeled diagram for problems involving geometry. Your variables need to be clear. A primary equation. 3. A secondary equation for equations. Derivatives with step by step algebra. 5 Show setting those derivatives to zero $ determining where they are undefined.. 6 . The answer you get from the derivative may not be your final answer. So make sure to find the requested info. 2) Verify that your solution is indeed a may or min. You can use . a) first derivative numberline analysis 6) and derivative test F" ( x ) concave => max down P" ( x ) 20 - concave =) min up Don't forget to consider the endpoints. Sometimes they represent the extreme values needed to solve the problem .. NOTE The answers are included after each question.Try at least 6 problems . worksheet # 10 MAC 2311 Optimization Problems 1. The product of two positive numbers is 363. Minimize the sum of the first and three times the second, (answer: 33 and I1) 2. The management of a large store wishes to add a fenced-in rectangular storage yard of 20,000 sq. ft., using the building as one side of the yard. Find the minimum amount of fencing that must be used to enclose the remaining 3 sides of the yard. (answer. 400') 3. A farmer has 80 feet of fencing to enclose three sides of a rectangular plot of land (the fourth side has an existing stone partition). What dimensions for the rectangular plot will enclose the maximum area? (answer: 20'x40') 4. An open box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. Find the dimensions of the box of maximum volume if the material has dimensions 6 inches by 6 inches. (answer: 4" x 4" x 1") 5. An open box is to be made from a 16" by 30" piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box With largest possible volume? (Answer. 10/3") 6. An offshore oil well is located in the ocean at point W, which is 5 miles from the closest shorepoint A an a straight shoreline. The oil is to be piped to a shorepoint B that is 8 miles from A by piping it on a straight line under water from W to some shorepoint P.between A and B and 8KM