3.4 Applied Optimization Activity 3.4.2. A soup can in the shape of a right circular cylinder is to be made from two materials. The material for the side of the can costs $0.015 per square inch and the material for the lids costs $0.027 per square inch. Suppose that we desire to construct a can that has a volume of 16 cubic inches. What dimensions minimize the cost of the can? a. Draw a picture of the can and label its dimensions with appropriate variables. b. Use your variables to determine expressions for the volume, surface area, and cost of the can. c. Determine the total cost function as a function of a single variable. What is the domain on which you should consider this function? d. Find the absolute minimum cost and the dimensions that produce this value.

Q: EN Suppose you are constructing a closed rectangular container with a volume of 30 ft2. The…

A: Volume of the rectangular container=30 ft3 Let l be length, b be breadth and 2l be height of…

Q: 3. You are tasked with designing a cylindrical can. The material for the top and bottom of the can…

A:

Q: 40. Minimizing cost. A rectangular garden measuring 1200 yd? is to be enclosed on two parallel sides…

A: Let x be the length and y be the width of the rectangular garden. The area is given by:…

Q: An open box is to be made from a rectangular piece of material by cutting equal squares from each…

A: Explanation of the answer is as follows

Q: 4. Suppose that we require a box of volume 2592 cubic inches with square top and bottom and…

A: The volume of the box is Cost of side material is  and top bottom material is

Q: A cylinder shaped can needs to be constructed to hold 350 cubic centimeters of soup. The material…

A:

Q: A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material…

A: We have to find Radius of the can, Height of the can and Minimum cost.

Q: It is required to build a mirror with the sides in the shape of a half circle, as shown in the…

A: Maximize area

Q: 9. You are building a bed for your cat. It will be a box with no lid that is twice as long as it is…

A:

Q: A rectangular parking area measuring 5000 ft? is to be enclosed on three sides using chain-link…

A: The explanation of answer as follows

Q: Problem 3: A company is designing a new container for its product. The container must have a volume…

A:

Q: SA E. John covered a cylindrical can with paper for a school project. The can is 20 centimeters tall…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: A rectangular page is to contain 24 square inches of print.  The margins at the top and bottom of…

A: From the given information, the area of the printed page is xy=24. xy=24y=24x The length of the…

Q: A pencil cup with a capacity of 33 in.3 is to be constructed in the shape of a right circular…

A: Volume of the cup (V) = 33 in3  Material for sides costs = 29 c/in2  Material for base costs = 46…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.