exam1 - 1 IE 220 Fall 2007 Professor Snyder October 4 2007...

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1 IE 220 Fall 2007 Professor Snyder October 4, 2007 Name: Mid-Term Exam 1 INSTRUCTIONS: Write neatly and show your work for each question. I will give partial credit for partial answers. You may not use your notes, slides, or textbook. You may use a calculator. The exam contains a few Fail Safes . If you cannot solve a problem whose solution is required to complete the subsequent problems, you may opt instead to use the Fail Safe as the solution to the problem. The solutions specified by the Fail Safes are incorrect , but you may proceed as though they are correct. I will still give partial credit for the incorrect answer that you provided for the earlier question. If you need more space, use the back of the page or come see me and I will give you more paper. You may remove the staple if you wish. Please put the pages back in the correct order at the end of the exam. There are 100 total points. Good luck!
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2 1. ( 46 points ) Dorwyn Glass has won the contract to supply doors and windows for the new Sands Casino in Bethlehem. Since casinos typically have very few windows, we’ll concentrate on doors in this problem. To manufacture hardware (handles, hinges, etc.) for the doors, Dorwyn blends three metals to form an alloy (a mixture of metals). The table below lists the density, the carbon and phosphorus content, and the price per kg, of each of the three metals. The characteristics of the alloy are all proportional to the amount of the three metals. For example, if the alloy is composed of 20% metal 1, 30% metal 2, and 50% metal 3, then it has a density of 0 . 2 × 6000+0 . 3 × 5500+0 . 5 × 7000 = 6350, a carbon content of 18%, and a price of $1.90. Metal Density Carbon (%) Phosphorus (%) Price ($/kg) 1 6000 20 5 $2.00 2 5500 30 1 $2.50 3 7000 10 6 $1.50 To meet design specifications, the resulting alloy must satisfy certain requirements: The density must be at most 6000. The carbon content must be at least 25%. The phosphorus content must be exactly 5%. Let x i represent the percentage of the alloy that is composed of metal i , i = 1 , 2 , 3. For example, if x 2 = 0 . 3, then 30% of the alloy is made up of metal 2.
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exam1 - 1 IE 220 Fall 2007 Professor Snyder October 4 2007...

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