Test 1 Version 1 Solutions

# Test 1 Version 1 Solutions - IE 280 Spring 2008 lg “lg...

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Unformatted text preview: IE 280 Spring 2008 lg “lg lOWl‘x / Name SQ] HQ Test 1 Version 1 Complete this exam. You may have one 8.5” x 11” page of notes but no calculator. Turn your cell phone and/or other electronic communications devices off. 1. Solve the following LP using the graphical method. You must Show your work in order to get credit. Don’t forget to show and label all extreme points. (25pm) min 2 = 3x, +6x2 s.t. 2x1 +9x2 S 12 3x1+2x2 S 9 x1 —x2 \$1 x1,x2 20 30 How many optimal solutions are there? (circle ONE) NONE. MORE THAN ONE If there is one or more than one optimal solution, report at least one of them here. At an optimal solution, x] = O 2. The Whitt Window Company is a company with only three employees. This company only makes two types of windows: a wood-framed window and an aluminum-framed window. Each wood-framed window sold results in \$60 proﬁt and each aluminum-framed window sold results in \$30 proﬁt. Doug makes the wood frames and can make 6 per day. Linda makes the aluminum frames and can make 4 per day. Bob forms and cuts the glass and can produce 48 square feet of glass per day. Each wood-framed window uses 6 square feet of glass and each aluminum-framed window uses 8 square feet of glass. Formulate a linear program to determine how Whitt Window Company should maximize its proﬁt. prts) DO NOT SOLVE THE RESULTING LP! ! l! (10 3. A hardware store packages handyman bags of screws, bolts, nuts and washers. Screws come in 100 lb. boxes which cost \$110 each. Bolts come in 100 lb. boxes which cost \$150 each. Nuts come in 80 lb. boxes which cost \$70 each. Washers come in 30 1b. boxes which cost \$20. The handyman packages must weigh at least one pound each and must include, by weight, at least 10% screws and 25% bolts, and at most 15% nuts and 10% washers. Formulate an LP to help the store package their handyman bags, assuming all bags are the same. WWO [118*It5b439‘n1‘gw wﬁﬂuﬁmusf‘ sﬂL 31—194 ntw 21 {acad- lb 2 . ha a 0.1%“ WWW) W f 0.!OCSﬁlg ﬂ+W) ...
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