# Calculus - optimization

**Question description**

1. You with to build a greenhouse. The ends of the greenhouse are to be shaped like a trapezoid with the outer walls at a 45* angle with the ground. THe height of the center of the greenhouse is 12 ft. You require the volume of the greenhouse to be 3456 ft^{3}. What are the dimensions of the greenhouse that minimize cost? (Assume all walls/floors cost the same.)

3. A passenger boat uses $432 worth of fuel per hour when cruising at 12 mph. The cost of fuel is proportional to the cube of the speed. Aside from the cost of fuel, the cost of running this boat (labor, maintenance, etc) is $691.20 per hour. How fast should the boat travel to minimize the cost per mile travelled?

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