Unformatted text preview: Sample questions from IE 280, spring 2007 corresponding to IE 280 Spring 2008 Unit 1 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. (25 pts) max z = 5 x1 + 4 x2 s.t. 3 x1 + 2 x2 12 x1 + 2 x2 6  x1 + x2 1 x1 , x2 0 How many solutions are there? (circle ONE) NONE ONE MORE THAN ONE If there is one solution, report it here. At the optimal solution, x1 = _______________ x2 = _______________ z = _______________ 2. Alumco manufactures aluminum sheets and aluminum bars. The maximum production capacity is estimated at either 800 sheets or 600 bars per day, however, both aluminum sheets and bars can be made in each day. The maximum daily demand is 550 sheets and 580 bars. The profit is $40 per sheet and $35 per bar. Formulate a linear program to determine how Alumco should maximize his profit. (25 pts) DO NOT SOLVE THE RESULTING LP!!!! Sample questions from IE 280, spring 2007 corresponding to IE 280 Spring 2008 Unit 2 3. A hospital employs volunteers to staff the reception desk between 8 am and 10 pm. Each volunteer works 3 consecutive hours except for those starting at 8 pm, who work for 2 hours. Volunteers can start working at the following times: 8 am, 10 am, 1 pm, 3 pm, 5 pm and 8 pm. Because of limited space in the reception area, the number of volunteers must be kept at a minimum. The following table tells how many volunteers are needed in each time period. Hour 89 am 910 am 1011 am 11 am noon Noon 1 pm 1 2 pm 2 3 pm 3 4 pm 4 5 pm 5 6 pm 67 pm 78 pm 89 pm 910 pm number of volunteers needed 4 4 6 6 8 8 6 6 4 4 6 6 8 8 Formulate an LP to help the hospital schedule the volunteers. 4. HiV produces three types of canned juice drinks A, B and C using fresh strawberries, grapes and apples. The daily supply is limited to 200 tons of strawberries, 100 tons of grapes and 150 tons of apples. The cost per ton is $200 per ton of strawberries, $100 per ton of grapes and $90 per ton of apples. One tons of each fruit yields 1500 lb of strawberry juice, 1200 lb of grape juice and 1000 lb of apple juice. Drink A is made of equal parts of strawberry and apple juice. Drink B is made of 25% strawberry juice, 25% grape juice and 50% apple juice. Drink C is made of 40% grape juice and 60% apple juice. All drinks are sold in 1 lb cans. The price per can is $1.15, $1.25 and $1.20 for drinks A, B, and C. Formulate an LP to determine the optimal mix of the three drinks. . ...
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 Spring '08
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 $40, apple juice, $35

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