takehome3-1 - homework assignments 3 NEVER use a letter...

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Exam 3: Takehome Problem M170-003 Spring, 2008 Name: Problem: A large chemical storage tank is to be built in a shape of a cylinder as shown at right. Assume the following facts about cost. Cost (per ft 2 ) of the Foor is an unknown constant. Call it k $/ft 2 . Cost of the curved side wall (per square foot of surface area) is 1.8 times the cost (per ft 2 ) of the Foor. Cost of the roof (per square foot of surface area) is 2.6 times the cost (per ft 2 ) of the Foor. If the total volume is ±xed at V ft 3 , what is the cost of the cheapest tank? Further instructions: 1. Write up your solution on your own paper. Staple this sheet to the front. 2. You must show (and show work for) all six stages of the solution as outlined in previous
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Unformatted text preview: homework assignments. 3. NEVER use a letter without de±ning what it measures or stands for. 4. This is worth 20 of the 100 points on your next exam. 5. BONUS: ²or another 2 bonus points, compute the ratio of height to diameter for the cheapest tank. Simplify your answer as exactly and as far as possible. 6. HINT: If you are having trouble, practice with numbers instead of letters. ²or instance, if you use k = 10 $/ft 2 and V = 1 . 5 million ft 3 , you should get a tank with radius 62.035 feet at a cost of $1.306 million. 1...
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