assignment1-1

# assignment1-1 - compatible with the model prod.mod Then use...

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ORIE 3300/5300 ASSIGNMENT 1 Fall 2011 Due: 11am, Tuesday September 6. This assignment is individual work. 1. Read pages 2–11 of the AMPL book. 2. The Student Edition of AMPL on the AMPL website includes a MODELS folder containing many useful models. Read through the ﬁle prod.mod : this question asks you to use this model to solve a particular linear program. An oil reﬁnery can produce 3 types of gasoline: “Regular”, “Plus”, and “Ultra”. It can produce Regular at 10000 gallons per hour, for a proﬁt of 10 cents per gallon, or Plus at 9000 gallons per hour, for a proﬁt of 11 cents per gallon, or Ultra at 8500 gallons per hour, for a proﬁt of 12 cents per gallon. The reﬁnery operates 24 hours a day, and can ship at most 120000 gallons of each type of gasoline each day. We wish to maximize proﬁt. Specify this problem in an AMPL data ﬁle called smog.dat

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Unformatted text preview: , compatible with the model prod.mod . Then use AMPL to solve the problem. Print out your data ﬁle and AMPL output. 3. Consider the following linear program. maximize 9 x 1 + 8 x 2 subject to x 1-x 2 ≤ 2 3 x 1 + x 2 ≤ 10 x 1 + 2 x 2 ≤ 10 x 1 , x 2 ≥ . Find the optimal solution graphically. By adding together suitable multiples of the constraints, prove algebraically that your answer is indeed optimal. 1 4. For each of the following linear programs, decide graphically whether the problem is infeasible, unbounded, or has an optimal solution. Then explain algebraically why your answer is correct. (i) maximize-x 2 subject to x 1 + x 2 ≥ 1 x 1-x 2 ≤ -3 x 2 ≤ 1 (ii) maximize-x 2 subject to x 1 + x 2 ≥ 1 x 1-x 2 ≤ -3 x 2 ≥ 1 (iii) maximize x 2 subject to x 1 + x 2 ≥ 1 x 1-x 2 ≤ -3 x 2 ≥ 1 2...
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assignment1-1 - compatible with the model prod.mod Then use...

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