1. A rectangular field is going to be enclosed and divided into two separate rectangular areas. (The areas do not have to be equal.) Find the minimum fencing that is required if the total area of the field is 1200 m2.
2. A closed cylindrical container needs to have a volume of 128pie dm3. Find the dimensions if the total area must be a minimum.
3. A rectangular storage box has a base that is three times as long as it is wide. The top is made of a material that costs 35 times the price per square meter of the material used for the rest of the box. Find the dimensions that would be necessary to ensure the minimal cost if the volume of the box must be 3 m3.
4. The Meal Group Caterer finds that competitors cater lunch for a group of 100 people for $5 each. The manager of Meal Group Caterer calculates that for each 25 cent discount per lunch, it is possible to sell an additional 10 lunches. If each lunch costs Meal Group Caterer $2 to prepare, how many lunches should be prepared to maximize the profit?