FINAL EXAM REVIEW QUESTIONS - TOMORROW FINAL EXAM IN THE MORNING!
PLEASE HELP SO I CAN FOLLOW YOUR SOLUTIONS.
1 The management of the UNICO department store has decided to enclose an 841 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $6/running foot and the steel fencing costs $3/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)
wood side 1 ft steel side 2 ft
2 By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 15 in. long and 8 in. wide, find the dimensions of the box that will yield the maximum volume. (Round your answers to two decimal places.)
1 in (smallest value) 2 in
3 in (largest value)
3 If an open box has a square base and a volume of 98 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. (Round your answers to two decimal places.) height 1 in length 2 in width 3 in
4 A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 35¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 15¢/square foot, determine the dimensions of the box that can be constructed at minimum cost.
x = 1 ft y = 2 ft
5 A Norman window has the shape of a rectangle surmounted by a semicircle (see the figure below). If a Norman window is to have a perimeter of 34 ft, what should its dimensions be in order to allow the maximum amount of light through the window? (Round your answers to two decimal places.)
x = 1 ft
y = 2 ft
6 The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $336/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 100) for the cruise, then each fare is reduced by $4 for each additional passenger.
Assuming at least 20 people sign up for the cruise, determine how many passengers will result in the maximum revenue for the owner of the yacht.
What is the maximum revenue?
What would be the fare/passenger in this case? (Round your answer to the nearest dollar.)
3 dollars per passenger