1. A resort is roping of a children's swimming area in the lakeat the resort. They have 150m of rope to use. What is the maximumarea they can rope off for the children's swimming section,assuming that they do not need to run the rope along the beach sideof the area? (use optimization)
2. Vivian makes hand made soap and sells them at a craft shows.She found that at one show she sold 450 soaps at $4 per bar. Afterdoing some research she finds that for every $0.25 reduction inprice she will sell an additional 20 soaps. What price willmaximize her sails?
3. A city is setting up a community garden plot for residentsliving in apartments. The plots will be arranged as shown and eachwill be 24m^2. ( 4 rows 5 columns) Fencing will run between theplots and around the entire garden. The fencing between the lotscosts $4/m and the fencing around the entire costs $8/m.What shouldthe dimensions of the plots be to minimize the cost of thefencing?
