MAC 2233 Midterm: Exam-3-Additional-Review-Problems-MAC-2233

DIRECTION:

Show all work – facts, primary and secondary equations, finding the derivatives, doing sign tests, and don’t forget to answer the questions asked!

1. A pipeline is to be run to a resort community which is on an island 16 miles from the closest point on the shoreline. The water source for the pipe is 30 miles down the shore. If it costs $500/mile to lay pipe through water and $300/mile to lay pipe on land, at what point on the shoreline should the pipe turn into the water to minimize cost? What is the total cost? (see diagram)

2. A rectangular cardboard poster is to contain 216 square inches of printed matter with 2-inch margins at the sides and 3-inch margins at the top and bottom. Find the dimensions of the poster using the least amount of cardboard.

3. A poster is to have a total area of 125 square inches. The printed material is to be surrounded by a margin of 3 inches on top and margins of 2 inches on the sides and the bottom. Find the dimensions of the poster that will maximize the area of the printed material.

1.) A rectangular area of 832 feet is to be surrounded on 3sides by a brick wall that costs $8 per foot and one side by afence that costs $5 per foot. FInd the dimensions of the garden sothe cost is minimized.

2.) A rectangular page is to have 64 square inches of print. Thepage has to have 4 inch margins on top and bottom, and a 1 inchmargin on each side. Find the dimensions of the page that minimizethe amount of paper used.