Optimization calculus.
A. Suppose the profit pattern for an office supply company that manufactures permanent markers is closely modeled by the function: P(x) = 8x - 0.001x2 - 5,000 , where the input is number of markers manufactured per month, and P is dollars per month. find the number of markers the company must sell in order to maximize their monthly profit?
B. Suppose a farmer wants to build a rectangular pen up against a fence. This means she only needs fencing for 3 sides of the pen instead of 4. If the farmer has 200 feet of fencing, what are the dimensions of the largest pen she can enclose?
C. Find the dimensions of the cylindrical water bottle with minimal surface area that can hold 16 cm3 of liquid.
SA= 2 π r2 + 2 π r h
V= π r2 h