Honors Calc BW
An open box is to be made from a piece of cardboard by cutting squares from the corners and folding the edges up. The cardboard is 10 inches on each side. Find the dimensions that will have a maximum volume. 1
1. An entrepreneur buys an apartment building with 40 units. The previous owner charged $240 per month for a single apartment and on average rented 32 apartments at that price. The entrepreneur discovers that for every $20 he raises the price another apartment stands vacant. What price should the entrepreneur charge for an apartment in order to maximize his revenue?
1. A grocer sells 50 loaves of bread a day. The cost is $0.65 a loaf. The grocer estimates that for each $0.05 price increase, 2 fewer loaves of bread will be sold. What cost will maximize the income?
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1. A Norman window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12 meters of framing materials what must the dimensions of the window be to let in the most light?
1. A farmer wants to build a rectangular fence that will enclose 120 square feet for his dog Miff. The two long sides of the fence are to be made of Styrofoam at a cost of $5 per foot. The two shorter sides are to be made of wire at a cost of $6 per foot. What are the dimensions of the fence that will minimize cost?
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1. We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft2 and the material used to build the sides cost $6/ft2. If the box must have a volume of 50 ft3 determine the dimensions that will minimize the cost to build the box.
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