In: Math
1. A resort is roping of a children's swimming area in the lake at the resort. They have 150m of rope to use. What is the maximum area they can rope off for the children's swimming section, assuming that they do not need to run the rope along the beach side of 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. After doing some research she finds that for every $0.25 reduction in price she will sell an additional 20 soaps. What price will maximize her sails?
3. A city is setting up a community garden plot for residents living in apartments. The plots will be arranged as shown and each will be 24m^2. ( 4 rows 5 columns) Fencing will run between the plots and around the entire garden. The fencing between the lots costs $4/m and the fencing around the entire costs $8/m.What should the dimensions of the plots be to minimize the cost of the fencing?