SOLUTION: 1. A rectangular piece of cardboard can be turned into an open box by cutting away identical squares from each corner and folding up the resulting flaps. The cardboard is 12 inche
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Question 1142996: 1. A rectangular piece of cardboard can be turned into an open box by cutting away identical squares from each corner and folding up the resulting flaps. The cardboard is 12 inches long and 12 inches wide.
a) Write an expression for the length of the box in terms of x (the length of each square you cut away).
b) Write an expression for the width of the box in terms of x.
c) Write an expression for the Volume of the box in terms of x.
d) Find the dimensions of the box that will yield the maximum volume.
2. A manufacturer of yoga pants sells them for $28 each. They hired some consultants who determined that the cost of manufacturing x pants was
C( x ) = x^2 − 2^x − 9.
a)Write a function for the revenue (the amount of money the company brings in).
b)Write a function for the profit (the revenue - cost).
c)Find the number of t-shirts they should make to maximize the profit function. Round your answer to the nearest whole number.
3. A man wishes to have a rectangular shaped garden in his backyard. He has 84 feet of fencing with which to enclose his garden.
a) Write an expression for the perimeter of the garden.
b) The area of the garden is A = l*w. Use the perimeter equation from part (a) to write the area in terms of just one variable.
c) Find the dimensions for the largest area garden he can have if he uses all the fencing. Answer by ikleyn(52780) (Show Source):
