1. CHOOSE ANY TWO of the following problems and determine i) the Optimization Function AND ii) the Boundary Interval: a) The Extreme Value Asian food truck sells 800 BBQ pork buns per week at a price of $1.50 each. For every S010 decrease in price, the number sold per week increases by 80. It costs $0.50 to make each bun and $1200 per month to rent the truck. Determine the price that will maximize the weekly profit. b) Centre Island is located 50 km across the lake directly south of the ferry terminal. Hippo Tours is located km east of the terminal and operates amphibious buses that can travel on land and water. The speed of the bus on land is 30 km/h and the speed in the water is 20 km/h. What is the shortest possible time for the trip to the island? c) A window has the shape of a rectangle with a right isosceles triangle on top. If the area of the window is to be 3 m², what dimensions of the rectangle and triangle will minimize the perimeter of the window? d) A rectangle is to be placed in the first quadrant, with one side on the x-axis and one side on the y-axis, so the rectangle lies below the line 2y + 6x = 18. Determine the dimensions of the rectangle that will yield a maximum area. e) A cylindrical wire frame has a wire circle for the top and bottom, and six straight wire rods that hold the top and bottom circles together. The total amount of wire used is 400 cm. What radius and height will maximize the volume enclosed by the frame?
1. CHOOSE ANY TWO of the following problems and determine i) the Optimization Function AND ii) the Boundary Interval: a) The Extreme Value Asian food truck sells 800 BBQ pork buns per week at a price of $1.50 each. For every S010 decrease in price, the number sold per week increases by 80. It costs $0.50 to make each bun and $1200 per month to rent the truck. Determine the price that will maximize the weekly profit. b) Centre Island is located 50 km across the lake directly south of the ferry terminal. Hippo Tours is located km east of the terminal and operates amphibious buses that can travel on land and water. The speed of the bus on land is 30 km/h and the speed in the water is 20 km/h. What is the shortest possible time for the trip to the island? c) A window has the shape of a rectangle with a right isosceles triangle on top. If the area of the window is to be 3 m², what dimensions of the rectangle and triangle will minimize the perimeter of the window? d) A rectangle is to be placed in the first quadrant, with one side on the x-axis and one side on the y-axis, so the rectangle lies below the line 2y + 6x = 18. Determine the dimensions of the rectangle that will yield a maximum area. e) A cylindrical wire frame has a wire circle for the top and bottom, and six straight wire rods that hold the top and bottom circles together. The total amount of wire used is 400 cm. What radius and height will maximize the volume enclosed by the frame?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please do A and B
Transcribed Image Text:Full Solutions
1. CHOOSE ANY TWO of the following problems and determine
i) the Optimization Function AND ii) the Boundary Interval:
a) The Extreme Value Asian food truck sells 800 BBQ pork buns per week at a price of $1.50 each. For every
S010 decrease in price, the number sold per week increases by 80. It costs $0.50 to make each bun and
$1200 per month to rent the truck. Determine the price that will maximize the weekly profit.
b) Centre Island is located 50 km across the lake directly south of the ferry terminal. Hippo Tours is located
30 km east of the terminal and operates amphibious buses that can travel on land and water. The speed of the
bus on land is 30 km/h and the speed in the water is 20 km/h. What is the shortest possible time for the trip to
the island?
c) A window has the shape of a rectangle with a right isosceles triangle on top. If the area of the window is to
be 3 m², what dimensions of the rectangle and triangle will minimize the perimeter of the window?
d) A rectangle is to be placed in the first quadrant, with one side on the x-axis and one side on the y-axis, so
the rectangle lies below the line 2y + 6x = 18. Determine the dimensions of the rectangle that will yield a
maximum area.
e) A cylindrical wire frame has a wire circle for the top and bottom, and six straight wire rods that hold the
top and bottom circles together. The total amount of wire used is 400 cm. What radius and height will
maximize the volume enclosed by the frame?
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