Only have to answer a minimum of 6 questions
MAC 2311 Optimization Problems MAC 2311 worksheet # 10 1. The product of two positive numbers is 363. Minimize the sum of the first and three times the strategy guide second. (answer: 33 and 11) 2. The management of a large store wishes to add a fenced-in rectangular storage yard of 20,000 sq. The following elements need to be a part 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') of solutions for optimization problems ( max / mins ) : 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 1 A carefully labeled diagram for problems maximum area? (answer: 20'x40') involving geometry. Your variables need 4 . An open box is to be made from a rectangular piece of material by cutting equal squares from each to be clear .. 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") 2 primary equation A secondary equation ( or equations ) 4 Derivatives with step by step algebra 5. An open box is to be made from a 16" by 30" piece of cardboard by cutting out squares of equal 5 Show setting those derivatives to zero & 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") determining where they are undefined The answer you get from the 6. An offshore oil well is located in the ocean at point W, which is 5 miles derivative may not be your final answer. from the closest shorepoint A an a straight shoreline. The oil is to be 5KM so, make sure to find the the requested into .. piped to a shorepoint B that is 8 miles from A by piping it on a straight 7) Verify that your solution is indeed line under water from W to some shorepoint P between A and B and 8KM then on to B via a pipe along the shoreline. If the cost of laying the pipe a may or min. You can use is $100,000 per mile under water and $75,000 per mile over land, where a) first derivative numberline analysis should the point P be located to minimize the cost of laying the pipe? 6) and d derivative test. (Answer: approx 5.67 miles from A) F" ( x ) max 7. The sum of the first number and twice the second number is 108 and the product is a maximum. down Find two positive numbers that satisfy this requirement. (Answer: 27 and 54) pli ( x ) 20 = concave = min 8 . Find the point on the graph of the function that is closest to the given point: up f(x) = x , 2.2) (Answer: (1,1) ) 8 Don't forget to consider the endpoints. Sometimes they represent the 9. A rancher has 400' of fencing with which to enclose two adjacent extreme values needed to solve rectangular corrals. What dimensions should be used so that the enclosed area will be a maximum? (Answer: 50' x 200/3') the problem .. 10. A Norman window is constructed by adjoining a semicircle NOTE The answers are included on the top of an ordinary rectangular window. Find the after each question . dimensions of the Norman window of maximum are if the total perimeter is 16 feet. (Answer: 32 'x _16 ") 4+1 -1
