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- The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch for the lateral surface and 2 cents per square inch for the bases. What is the total cost of constructing the box?An oil refinery is located on the north bank of a straight river that is 1 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 4 km east of the refinery. The cost of laying pipe is $300,000/km over land to a point P on the north bank and $600,000/km under the river to the tanks. To minimize the cost of the pipeline, how far (in km) from the refinery should P be located?An oil refinery is located 1 km north of a straight river that is2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of laying pipe is $400.00/km over land to a point P on the north bank and $800.00/km under the river to the tanks. To minimize the cost ofthe pipeline, where should P be located?
- 8. A closed rectangular tank with a square base and with capacity of 48 cu.m. is to be constructed. The material for the top and bottom costs Php 3,000 per square meter, for the sides Php 4,000 per square meter. What height of tank will give the minimum cost?The owner of a ranch wants to fence off a rectangular piece of land of area 30,000 square yards next to a river. No fencing will be used along the river. Thr land will be subdivided into 2 sections by means of a fence running perpendicular to the river. The fence costs $10 per yard. what should the dimensions be in order to minimize the total cost of the fence? List the dimensions in order of (side perpendicularto river) by (side parallel to river) what is the total cost of the fence? Thank you1. A farmer wants to fence off a rectangular field and use a well as one side. He has500 meters of fencing. What are the dimensions of the field that has the largestarea? 2.Two cars, one going due West at the rate of 100 km/hr and the other goingNorth at the rate of 70 km/hr, are traveling toward the intersection of the tworoads. At what rate are the cars approaching each other at the instant when thefirst car is0.3 km and the second car is 0.2 km from the intersection?
- A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $30 per linear meter to install. If the farmer wants to enclose 750 square meters of land, what dimensions will minimize the cost of the fence?a) If 1600 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. (include units) b) A rancher wants to fence in an area of 500000 square feet in a rectangular field and then divide it in half with a fence down the middle, parallel to one side. What is the shortest length of fence that the rancher can use?A gutter with trapezoidal cross section is to be made from a long strip of metal that is 22 cm wide, by bending the edges. If the base is to be 14 cm, what width at the top will give the maximum carrying capacity? Express your answer in whole number.
- I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $12 per foot, and the fencing for the east and west sides costs $6 per foot. If I have a budget of $120 for the project, what are the dimensions of the garden with the largest area I can enclose? --- smaller value x ----- larger value ? ft2A rectangular box is to have a square base and a volume of 24ft^3. If the material for the base costs $0.36/ft^2, the material for the sides costs $0.10/ft^2, and the material fort the top costs $0.24/ft^2, determine the dimensions of the box that can be constructed at minimum cost.A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $50/ft and on the other three sides by a metal fence costing $40/ft. If the area of the garden is 142 square feet, find the dimensions of the garden that minimize the cost. Length of side with bricks x= ????Length of adjacent side y=?????