Problem 1 MATLAB

Engineering Analysis Tools and Techniques ECE 102 Midterm Review Fall XXXX Problem 1 - Problem Solving and Modeling A steel storage tank for propane gas is to be designed in the shape of a cylinder with a hemisphere at each end as shown in the figure below. The construction cost to fabricate each end of the tank is $200 per square foot and the construction cost to fabricate the inner cylindrical portion of the tank is $100 per square foot. If the tank is to be designed to have a volume of 350 cubic feet, determine the dimensions of the tank that will minimize its cost of construction. Although this problem is completely different from the space shuttle insect container problem you completed earlier in the semester, the process of solving this problem is very similar. Let's review the heuristics that you used to solve the space shuttle insect problem. 1. Draw a simple diagram: For the insect container problem we drew diagrams that helped us visualize how the containers were arranged in the storage box. For this problem, it would be helpful to draw a diagram identifying the critical dimensions of the tank. Note that the radius of the inner cylindrical portion of the tank and the radius of the hemispheres at each end of the tank will be the same. 2. Identification of dependent and independent Variables: In the space shuttle insect problem we identified the independent and dependent variables that were necessary to compute the volume of each insect container as well as the size of each space shuttle cargo box. For this problem, you will want to identify a set of variables and parameters based on the dimensions you identified in the diagram you developed in step 1 that can be used to compute the volume of the tank and the cost of construction of the tank using the appropriate unit costs (S200 per square foot to fabricate the ends and S100 per square foot to fabricate the inner cylindrical portion). Remember, these unit costs are related to the surface area of the portion of the tank to be fabricated, not the tank's volume. Page 1 Engineering Analysis Tools and Techniques ECE 102 Midterm Review Fall XXXX Problem 1 - Problem Solving and Modeling A steel storage tank for propane gas is to be designed in the shape of a cylinder with a hemisphere at each end as shown in the figure below. The construction cost to fabricate each end of the tank is $200 per square foot and the construction cost to fabricate the inner cylindrical portion of the tank is $100 per square foot. If the tank is to be designed to have a volume of 350 cubic feet, determine the dimensions of the tank that will minimize its cost of construction. Although this problem is completely different from the space shuttle insect container problem you completed earlier in the semester, the process of solving this problem is very similar. Let's review the heuristics that you used to solve the space shuttle insect problem. 1. Draw a simple diagram: For the insect container problem we drew diagrams that helped us visualize how the containers were arranged in the storage box. For this problem, it would be helpful to draw a diagram identifying the critical dimensions of the tank. Note that the radius of the inner cylindrical portion of the tank and the radius of the hemispheres at each end of the tank will be the same. 2. Identification of dependent and independent Variables: In the space shuttle insect problem we identified the independent and dependent variables that were necessary to compute the volume of each insect container as well as the size of each space shuttle cargo box. For this problem, you will want to identify a set of variables and parameters based on the dimensions you identified in the diagram you developed in step 1 that can be used to compute the volume of the tank and the cost of construction of the tank using the appropriate unit costs (S200 per square foot to fabricate the ends and S100 per square foot to fabricate the inner cylindrical portion). Remember, these unit costs are related to the surface area of the portion of the tank to be fabricated, not the tank's volume. Page 1